Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-25T10:12:21.778Z Has data issue: false hasContentIssue false

References

Published online by Cambridge University Press:  29 September 2023

Masayuki Kawakita
Masayuki Kawakita
Affiliation:
Kyoto University, Japan
Get access

Summary

A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Complex Algebraic Threefolds , pp. 453 - 475
Publisher: Cambridge University Press
Print publication year: 2023

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abban, H., Fedorchuk, M. and Krylov, I.. Stability of fibrations over one-dimensional bases. Duke Math. J. 171 (2022), 2461–2518.Google Scholar
Abe, M. and Furushima, M.. On non-normal del Pezzo surfaces. Math. Nachr. 260 (2003), 3–13.Google Scholar
Ahmadinezhad, H.. Singular del Pezzo fibrations and birational rigidity. Automorphisms in birational and affine geometry, 3–15. Springer Proc. Math. Stat. 79, Springer, 2014.CrossRefGoogle Scholar
Ahmadinezhad, H.. On pliability of del Pezzo fibrations and Cox rings. J. Reine Angew. Math. 723 (2017), 101–125.CrossRefGoogle Scholar
Ahmadinezhad, H. and Zucconi, F.. Circle of Sarkisov links on a Fano 3-fold. Proc. Edinb. Math. Soc. (2) 60 (2017), 1–16.Google Scholar
Alekseev, V. A.. Rationality conditions for three-dimensional varieties with sheaf of del Pezzo surfaces of degree 4. Mat. Zametki 41 (1987), 724–730; translation in Math. Notes 41 (1987), 408–411.Google Scholar
Alexeev, V.. Two two-dimensional terminations. Duke Math. J. 69 (1993), 527–545.Google Scholar
Alexeev, V.. Boundedness and đŸ2 for log surfaces. Int. J. Math. 5 (1994), 779–810.Google Scholar
Altınok, S., Brown, G. and Reid, M.. Fano 3-folds, K3 surfaces and graded rings. Topology and geometry: Commemorating SISTAG, 25–53. Contemp. Math. 314, Am. Math. Soc., 2002.Google Scholar
Altman, A. and Kleiman, S.. Introduction to Grothendieck duality theory. Lecture Notes in Mathematics 146, Springer-Verlag, 1970.Google Scholar
Ambro, F.. Ladders on Fano varieties. J. Math. Sci. (N.Y.) 94 (1999), 1126–1135.Google Scholar
Ambro, F.. On minimal log discrepancies. Math. Res. Lett. 6 (1999), 573–580.CrossRefGoogle Scholar
Ambro, F.. The moduli b-divisor of an lc-trivial fibration. Compos. Math. 141 (2005), 385–403.Google Scholar
Ando, T.. On extremal rays of the higher dimensional varieties. Invent. Math. 81 (1985), 347–357.Google Scholar
Andreatta, M. and A. Wiƛniewski, J.. On contractions of smooth varieties. J. Algebraic Geom. 7 (1998), 253–312.Google Scholar
Artin, M.. Some numerical criteria for contractability of curves on algebraic surfaces. Am. J. Math. 84 (1962), 485–496.Google Scholar
Artin, M.. On isolated rational singularities of surfaces. Am. J. Math. 88 (1966), 129–136.Google Scholar
Artin, M.. On the solutions of analytic equations. Invent. Math. 5 (1968), 277–291.Google Scholar
Artin, M.. Algebraic approximation of structures over complete local rings. Publ. Math. Inst. Hautes Études Sci. 36 (1969), 23–58.Google Scholar
Artin, M.. The implicit function theorem in algebraic geometry. Algebraic geometry (Int. Colloq., Bombay, 1968), 13–34. Oxford University Press, 1969.Google Scholar
Artin, M.. Algebraization of formal moduli: II. Existence of modifications. Ann. Math. (2) 91 (1970), 88–135.Google Scholar
Artin, M. and Mumford, D.. Some elementary examples of unirational varieties which are not rational. Proc. Lond. Math. Soc. (3) 25 (1972), 75–95.Google Scholar
Arzhantsev, I., Derenthal, U., Hausen, J. and Laface, A.. Cox rings. Cambridge Studies in Advanced Mathematics 144, Cambridge University Press, 2015.Google Scholar
Atiyah, M. F.. On analytic surfaces with double points. Proc. R. Soc. Lond. Ser. A 247 (1958), 237–244.Google Scholar
Atiyah, M. F. and Bott, R.. A Lefschetz fixed point formula for elliptic complexes: II. Applications. Ann. Math. (2) 88 (1968), 451–491.Google Scholar
Atiyah, M. F. and Segal, G. B.. The index of elliptic operators: II. Ann. Math. (2) 87 (1968), 531–545.Google Scholar
Atiyah, M. F. and Singer, I. M.. The index of elliptic operators: I, III. Ann. Math. (2) 87 (1968), 484–530, 546–604.Google Scholar
Bădescu, L.. Algebraic surfaces. Translated from the 1981 Romanian original by MaƟek, V. and revised by the author. Universitext, Springer-Verlag, 2001.Google Scholar
Bănică, C. and StănăƟilă, O.. Algebraic methods in the global theory of complex spaces. Editura Academiei; John Wiley & Sons, 1976.Google Scholar
Barth, W. P., Hulek, K., Peters, C. A. M. and Van de Ven, A.. Compact complex surfaces. Second edition. Ergebnisse der Mathematik und ihrer Grenzgebiete (3) 4, Springer-Verlag, 2004.Google Scholar
Batyrev, V. V.. Stringy Hodge numbers of varieties with Gorenstein canonical singularities. Integrable systems and algebraic geometry, 1–32. World Scientific Publishing, 1998.Google Scholar
Batyrev, V. V.. Birational Calabi–Yau 𝑛-folds have equal Betti numbers. New trends in algebraic geometry, 1–11. London Math. Soc. Lecture Note Ser. 264, Cambridge University Press, 1999.Google Scholar
Beauville, A.. Prym varieties and the Schottky problem. Invent. Math. 41 (1977), 149–196.Google Scholar
Beauville, A.. VariĂ©tĂ©s de Prym et jacobiennes intermĂ©diaires. Ann. Sci. Éc. Norm. SupĂ©r. (4) 10 (1977), 309–391.Google Scholar
Beauville, A.. Complex algebraic surfaces. Translated from the 1978 French original by Barlow, R., with assistance from N. I. Shepherd-Barron and M. Reid. Second edition. London Mathematical Society Student Texts 34, Cambridge University Press, 1996.Google Scholar
Beauville, A.. The LĂŒroth problem. Rationality problems in algebraic geometry, 1–27. Lecture Notes in Math. 2172, Springer, 2016.Google Scholar
Beauville, A., Colliot-ThĂ©lĂšne, J.-L., Sansuc, J.-J. and Swinnerton-Dyer, P.. VariĂ©tĂ©s stablement rationnelles non rationnelles. Ann. Math. (2) 121 (1985), 283–318.Google Scholar
Beltrametti, M.. On the Chow group and the intermediate Jacobian of a conic bundle. Ann. Mat. Pura Appl. (4) 141 (1985), 331–351.Google Scholar
Berman, R. J.. K-polystability of Q-Fano varieties admitting KĂ€hler–Einstein metrics. Invent. Math. 203 (2016), 973–1025.Google Scholar
Berman, R. J., Boucksom, S. and Jonsson, M.. A variational approach to the Yau– Tian–Donaldson conjecture. J. Am. Math. Soc. 34 (2021), 605–652.Google Scholar
Berthelot, P., Grothendieck, A. and Illusie, L.. ThĂ©orie des intersections et thĂ©orĂšme de Riemann–Roch (SGA 6). Avec la collaboration Ferrand, de D., Jouanolou, J. P., Jussila, O., Kleiman, S., Raynaud et J. P. Serre, M.. Lecture Notes in Mathematics 225, Springer-Verlag, 1971.Google Scholar
Bingener, J.. Lokale ModulrÀume in der analytischen Geometrie. Band 1, 2. With the cooperation of Kosarew, S.. Aspects of Mathematics D2, D3, Friedr. Vieweg & Sohn, 1987.Google Scholar
Birkar, C.. On existence of log minimal models. Compos. Math. 146 (2010), 919–928.Google Scholar
Birkar, C.. On existence of log minimal models II. J. Reine Angew. Math. 658 (2011), 99–113.Google Scholar
Birkar, C.. Existence of log canonical flips and a special LMMP. Publ. Math. Inst. Hautes Études Sci. 115 (2012), 325–368.Google Scholar
Birkar, C.. Anti-pluricanonical systems on Fano varieties. Ann. Math. (2) 190 (2019), 345–463.Google Scholar
Birkar, C.. Singularities of linear systems and boundedness of Fano varieties. Ann. Math. (2) 193 (2021), 347–405.Google Scholar
Birkar, C., Cascini, P., Hacon, C. D. and McKernan, J.. Existence of minimal models for varieties of log general type. J. Am. Math. Soc. 23 (2010), 405–468.Google Scholar
Blum, H., Liu, Y. and Xu., C. Openness of K-semistability for Fano varieties. Duke Math. J. 171 (2022), 2753–2797.Google Scholar
Bogomolov, F. A.. Holomorphic tensors and vector bundles on projective varieties. Izv. Akad. Nauk SSSR Ser. Mat. 42 (1978), 1227–1287; translation in Math. USSR-Izv. 13 (1979), 499–555.Google Scholar
Bombieri, E.. Canonical models of surfaces of general type. Publ. Math. Inst. Hautes Études Sci. 42 (1973), 171–219.CrossRefGoogle Scholar
Bombieri, E. and Catanese, F.. The tricanonical map of a surface with đŸ2 = 2, 𝑝𝑔 = 0. C. P. Ramanujam – a tribute, 279–290. Tata Inst. Fund. Res. Stud. Math. 8, Springer, 1978.Google Scholar
Borel, A. and Serre, J.-P.. Le thĂ©orĂšme de Riemann–Roch. Bull. Soc. Math. France 86 (1958), 97–136.Google Scholar
Borisov, A. A. and Borisov, L. A.. Singular toric Fano varieties. Mat. Sb. 183 (1992), 134–141; translation in Sb. Math. 75 (1993), 277–283.Google Scholar
Boucksom, S., Demailly, J.-P., Păun, M. and Peternell, T.. The pseudo-effective cone of a compact KĂ€hler manifold and varieties of negative Kodaira dimension. J. Algebraic Geom. 22 (2013), 201–248.Google Scholar
Bourbaki, N.. ÉlĂ©ments de mathĂ©matique. AlgĂšbre. Chapitre 9. Reprint of the 1959 original. Springer-Verlag, 2007.CrossRefGoogle Scholar
Brieskorn, E.. Über die Auflösung gewisser SingularitĂ€ten von holomorphen Abbildungen. Math. Ann. 166 (1966), 76–102.Google Scholar
Brieskorn, E.. Rationale SingularitĂ€ten komplexer FlĂ€chen. Invent. Math. 4 (1967/68), 336–358.Google Scholar
Brieskorn, E.. Die Auflösung der rationalen SingularitĂ€ten holomorpher Abbildungen. Math. Ann. 178 (1968), 255–270.Google Scholar
Bruce, J. W. and Wall, C. T. C.. On the classification of cubic surfaces. J. Lond. Math. Soc. (2) 19 (1979), 245–256.Google Scholar
Bruns, W. and Herzog, J.. Cohen–Macaulay rings. Revised edition. Cambridge Studies in Advanced Mathematics 39, Cambridge University Press, 1998.Google Scholar
Buchsbaum, D. A. and Eisenbud, D.. Algebra structures for finite free resolutions, and some structure theorems for ideals of codimension 3. Am. J. Math. 99 (1977), 447–485.Google Scholar
Burch, L.. On ideals of finite homological dimension in local rings. Proc. Camb. Philos. Soc. 64 (1968), 941–948.Google Scholar
Campana, F.. ConnexitĂ© rationnelle des variĂ©tĂ©s de Fano. Ann. Sci. Éc. Norm. SupĂ©r. (4) 25 (1992), 539–545.Google Scholar
Campana, F., Koziarz, V. and Păun, M.. Numerical character of the effectivity of adjoint line bundles. Ann. Inst. Fourier (Grenoble) 62 (2012), 107–119.Google Scholar
Cartan, H.. Quotient d’un espace analytique par un groupe d’automorphismes. Algebraic geometry and topology, 90–102. Princeton University Press, 1957.Google Scholar
Cartan, H.. Quotients of complex analytic spaces. Contributions to function theory (Int. Colloq., Bombay, 1960), 1–15. Tata Inst. Fund. Res., 1960.Google Scholar
Carter, R., Segal, G. and Macdonald, I.. Lectures on Lie groups and Lie algebras. London Mathematical Society Student Texts 32, Cambridge University Press, 1995.Google Scholar
Cascini, P. and Tasin, L.. On the Chern numbers of a smooth threefold. Trans. Am. Math. Soc. 370 (2018), 7923–7958.Google Scholar
Catanese, F.. Pluricanonical mappings of surfaces with đŸ2 = 1, 2, 𝑞 = 𝑝𝑔 = 0. Algebraic surfaces, 247–266. C.I.M.E. Summer Sch. 76, Springer, 2010.Google Scholar
Cheltsov, I.. Nonrational nodal quartic threefolds. Pacific J. Math. 226 (2006), 65–81.Google Scholar
Cheltsov, I.. Log canonical thresholds of del Pezzo surfaces. Geom. Funct. Anal. 18 (2008), 1118–1144.Google Scholar
Cheltsov, I. A.. Extremal metrics on two Fano manifolds. Mat. Sb. 200 (2009), 97–136; translation in Sb. Math. 200 (2009), 95–132.Google Scholar
Cheltsov, I.. Factorial threefold hypersurfaces. J. Algebraic Geom. 19 (2010), 781–791.CrossRefGoogle Scholar
Cheltsov, I. and Grinenko, M.. Birational rigidity is not an open property. Bull. Korean Math. Soc. 54 (2017), 1485–1526.Google Scholar
Cheltsov, I. and Park, J.. Birationally rigid Fano threefold hypersurfaces. Mem. Am. Math. Soc. 246, no 1167, (2017).Google Scholar
Chen, J.-J.. On threefold canonical thresholds. Adv. Math. 404 (2022), 108447, 36pp.CrossRefGoogle Scholar
Chen, J. A. and Chen, M.. Explicit birational geometry of threefolds of general type, I. Ann. Sci. Éc. Norm. SupĂ©r. (4) 43 (2010), 365–394.Google Scholar
Chen, J. A. and Chen, M.. Explicit birational geometry of 3-folds of general type, II. J. Differ. Geom. 86 (2010), 237–271.Google Scholar
Chen, J. A. and Chen, M.. Explicit birational geometry of 3-folds and 4-folds of general type, III. Compos. Math. 151 (2015), 1041–1082.Google Scholar
Chen, J. A., Chen, M. and Zhang, D.-Q.. The 5-canonical system on 3-folds of general type. J. Reine Angew. Math. 603 (2007), 165–181.Google Scholar
Chen, M.. On the Q-divisor method and its application. J. Pure Appl. Algebra 191 (2004), 143–156.Google Scholar
Chen, M.. On minimal 3-folds of general type with maximal pluricanonical section index. Asian J. Math. 22 (2018), 257–268.Google Scholar
Chen, X., Donaldson, S. and Sun, S.. KĂ€hler–Einstein metrics on Fano manifolds. III: Limits as cone angle approaches 2𝜋 and completion of the main proof. J. Am. Math. Soc. 28 (2015), 235–278.Google Scholar
Chern, S.-S.. Characteristic classes of Hermitian manifolds. Ann. Math. (2) 47 (1946), 85–121.Google Scholar
Chevalley, C.. Invariants of finite groups generated by reflections. Am. J. Math. 77 (1955), 778–782.Google Scholar
Clemens, C. H.. Double solids. Adv. Math. 47 (1983), 107–230.Google Scholar
Clemens, C. H. and Griffiths, P. A.. The intermediate Jacobian of the cubic three-fold. Ann. Math. (2) 95 (1972), 281–356.Google Scholar
Colliot-ThĂ©lĂšne, J.-L.. ArithmĂ©tique des variĂ©tĂ©s rationnelles et problĂšmes birationnels. Proceedings of the International Congress of Mathematicians (Berkeley, 1986). Vol. 1, 641–653. Am. Math. Soc., 1987.Google Scholar
Colliot-ThĂ©lĂšne, J.-L. and Pirutka, A.. Hypersurfaces quartiques de dimension 3: Non-rationalitĂ© stable. Ann. Sci. Éc. Norm. SupĂ©r. (4) 49 (2016), 371–397.Google Scholar
Corti, A.. Factoring birational maps of threefolds after Sarkisov. J. Algebraic Geom. 4 (1995), 223–254.Google Scholar
Corti, A.. Del Pezzo surfaces over Dedekind schemes. Ann. Math. (2) 144 (1996), 641–653.Google Scholar
Corti, A.. Singularities of linear systems and 3-fold birational geometry. Explicit birational geometry of 3-folds, 259–312. London Math. Soc. Lecture Note Ser. 281, Cambridge University Press, 2000.Google Scholar
Corti, A., ed. Flips for 3-folds and 4-folds. Oxford Lecture Series in Mathematics and its Applications 35, Oxford University Press, 2007.Google Scholar
Corti, A. and Mella, M.. Birational geometry of terminal quartic 3-folds, I.Am. J. Math. 126 (2004), 739–761.Google Scholar
Corti, A., Pukhlikov, A. and Reid, M.. Fano 3-fold hypersurfaces. Explicit birational geometry of 3-folds, 175–258. London Math. Soc. Lecture Note Ser. 281, Cambridge University Press, 2000.Google Scholar
Corti, A. and Reid, M., eds. Explicit birational geometry of 3-folds. London Mathematical Society Lecture Note Series 281, Cambridge University Press, 2000.CrossRefGoogle Scholar
Cutkosky, S.. Elementary contractions of Gorenstein threefolds. Math. Ann. 280 (1988), 521–525.Google Scholar
Cutkosky, S. D. and Srinivas, V.. On a problem of Zariski on dimensions of linear systems. Ann. Math. (2) 137 (1993), 531–559.Google Scholar
Danilov, V. I.. Birational geometry of toric 3-folds. Izv. Akad. Nauk SSSR Ser. Mat. 46 (1982), 971–982; translation in Math. USSR-Izv. 21 (1983), 269–280.Google Scholar
Debarre, O.. Higher-dimensional algebraic geometry. Universitext, Springer-Verlag, 2001.Google Scholar
de Fernex, T.. Birationally rigid hypersurfaces. Invent. Math. 192 (2013), 533– 566; erratum ibid. 203 (2016), 675–680.Google Scholar
de Fernex, T. L. Ein and Mustaƣă, M.. Multiplicities and log canonical threshold. J. Algebraic Geom. 13 (2004), 603–615.Google Scholar
Denef, J. and Loeser, F.. Germs of arcs on singular algebraic varieties and motivic integration. Invent. Math. 135 (1999), 201–232.Google Scholar
Dimca, A.. Betti numbers of hypersurfaces and defects of linear systems. Duke Math. J. 60 (1990), 285–298.Google Scholar
Dolgachev, I.. Weighted projective varieties. Group actions and vector fields, 34–71. Lecture Notes in Math. 956, Springer, 1982.Google Scholar
Donaldson, S. K.. Anti self-dual Yang–Mills connections over complex algebraic surfaces and stable vector bundles. Proc. Lond. Math. Soc. (3) 50 (1985), 1–26.Google Scholar
Donaldson, S. K.. Scalar curvature and stability of toric varieties. J. Differ. Geom. 62 (2002), 289–349.Google Scholar
Douady, A.. Le problĂšme des modules pour les sous-espaces analytiques compacts d’un espace analytique donnĂ©. Ann. Inst. Fourier (Grenoble) 16 (1966), 1–95.Google Scholar
Ducat, T.. Mori extractions from singular curves in a smooth 3-fold. PhD thesis, University of Warwick, 2015.Google Scholar
Ducat, T.. Divisorial extractions from singular curves in smooth 3-folds. Int. J. Math. 27 (2016), 1650005, 23pp.Google Scholar
Ducat, T.. Constructing Q-Fano 3-folds à la Prokhorov & Reid. Bull. Lond. Math. Soc. 50 (2018), 420–434.Google Scholar
Durfee, A. H.. Fifteen characterizations of rational double points and simple critical points. Enseign. Math. 25 (1979), 131–163.Google Scholar
Ein, L. and Lazarsfeld, R.. Global generation of pluricanonical and adjoint linear series on smooth projective threefolds. J. Am. Math. Soc. 6 (1993), 875–903.Google Scholar
Ein, L., Lazarsfeld, R., Mustaƣă, M., Nakamaye, M. and Popa, M.. Restricted volumes and base loci of linear series. Am. J. Math. 131 (2009), 607–651.Google Scholar
Ein, L. and Mustaƣă, M.. Inversion of adjunction for local complete intersection varieties. Am. J. Math. 126 (2004), 1355–1365.Google Scholar
Ein, L., Mustaƣă, M. and Yasuda, T.. Jet schemes, log discrepancies and inversion of adjunction. Invent. Math. 153 (2003), 519–535.Google Scholar
Eisenbud, D.. Homological algebra on a complete intersection, with an application to group representations. Trans. Am. Math. Soc. 260 (1980), 35–64.Google Scholar
Eisenbud, D.. Commutative algebra. With a view toward algebraic geometry. Graduate Texts in Mathematics 150, Springer-Verlag, 1995.Google Scholar
Eisenbud, D. and Harris, J.. 3264 and all that. A second course in algebraic geometry. Cambridge University Press, 2016.Google Scholar
Ekedahl, T.. Foliations and inseparable morphisms. Algebraic geometry, Bowdoin, 1985, 139–149. Proc. Sympos. Pure Math. 46, Part 2, Am. Math. Soc., 1987.Google Scholar
Endraß, S.. On the divisor class group of double solids. Manuscripta Math. 99 (1999), 341–358.Google Scholar
Fischer, G.. Complex analytic geometry. Lecture Notes in Mathematics 538, Springer-Verlag, 1976.Google Scholar
Flenner, H.. Divisorenklassengruppen quasihomogener SingularitĂ€ten. J. Reine Angew. Math. 328 (1981), 128–160.Google Scholar
Francia, P.. Some remarks on minimal models I. Compos. Math. 40 (1980), 301– 313.Google Scholar
Fujiki, A.. Deformation of uniruled manifolds. Publ. Res. Inst. Math. Sci. 17 (1981), 687–702.Google Scholar
Fujino, O.. Termination of 4-fold canonical flips. Publ. Res. Inst. Math. Sci. 40 (2004), 231–237; addendum ibid. 41 (2005), 251–257.Google Scholar
Fujino, O.. On the Kleiman–Mori cone. Proc. Jpn. Acad. Ser. A Math. Sci. 81 (2005), 80–84.Google Scholar
Fujino, O.. Fundamental theorems for the log minimal model program. Publ. Res. Inst. Math. Sci. 47 (2011), 727–789.Google Scholar
Fujino, O.. On Kawamata’s theorem. Classification of algebraic varieties, 305–315. EMS Ser. Congr. Rep., Eur. Math. Soc., 2011.Google Scholar
Fujino, O.. Foundations of the minimal model program. MSJ Memoirs 35, Mathematical Society of Japan, 2017.Google Scholar
Fujino, O.. Semipositivity theorems for moduli problems. Ann. Math. (2) 187 (2018), 639–665.Google Scholar
Fujino, O. and Gongyo, Y.. On canonical bundle formulas and subadjunctions. Michigan Math. J. 61 (2012), 255–264.Google Scholar
Fujino, O. and Mori, S.. A canonical bundle formula. J. Differ. Geom. 56 (2000), 167–188.Google Scholar
Fujino, O. and Sato, H.. Introduction to the toric Mori theory. Michigan Math. J. 52 (2004), 649–665.Google Scholar
Fujita, K.. A valuative criterion for uniform K-stability of Q-Fano varieties. J. Reine Angew. Math. 751 (2019), 309–338.Google Scholar
Fujita, T.. On the structure of polarized manifolds with total deficiency one, I, II, III. J. Math. Soc. Jpn. 32 (1980), 709–725, 33 (1981), 415–434, 36 (1984), 75–89.Google Scholar
Fujita, T.. Fractionally logarithmic canonical rings of algebraic surfaces. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 30 (1984), 685–696.Google Scholar
Fujita, T.. Problems. Birational geometry of algebraic varieties. Open problems, 42–45. The 23rd International Symposium, Division of Mathematics, Taniguchi Foundation, 1988.Google Scholar
Fulton, W.. Introduction to toric varieties. Annals of Mathematics Studies 131, Princeton University Press, 1993.Google Scholar
Fulton, W.. Intersection theory. Second edition. Ergebnisse der Mathematik und ihrer Grenzgebiete (3) 2, Springer-Verlag, 1998.Google Scholar
Giblin, P. J.. On the singularities of two related hypersurfaces. J. Lond. Math. Soc. (2) 7 (1973), 367–375.Google Scholar
Gizatullin, M. H.. Rational đș-surfaces. Izv. Akad. Nauk SSSR Ser. Mat. 44 (1980), 110–144; translation in Math. USSR-Izv. 16 (1981), 103–134.Google Scholar
Gongyo, Y.. On the minimal model theory for dlt pairs of numerical log Kodaira dimension zero. Math. Res. Lett. 18 (2011), 991–1000.Google Scholar
Goresky, M. and MacPherson, R.. Stratified Morse theory. Ergebnisse der Mathematik und ihrer Grenzgebiete (3) 14, Springer-Verlag, 1988.Google Scholar
Goto, S., Nishida, K. and Watanabe, K.-i. Non-Cohen–Macaulay symbolic blowups for space monomial curves and counterexamples to Cowsik’s question. Proc. Am. Math. Soc. 120 (1994), 383–392.Google Scholar
Graber, T., Harris, J. and Starr, J.. Families of rationally connected varieties. J. Am. Math. Soc. 16 (2003), 57–67.Google Scholar
Grauert, H.. Über Modifikationen und exzeptionelle analytische Mengen. Math. Ann. 146 (1962), 331–368.Google Scholar
Grauert, H.. Über die Deformation isolierter SingularitĂ€ten analytischer Mengen. Invent. Math. 15 (1972), 171–198.Google Scholar
Grauert, H.. Der Satz von Kuranishi fĂŒr kompakte komplexe RĂ€ume. Invent. Math.25 (1974), 107–142.Google Scholar
Grauert, H. and Remmert, R.. Coherent analytic sheaves. Grundlehren der mathematischen Wissenschaften 265, Springer-Verlag, 1984.Google Scholar
Grauert, H. and Riemenschneider, O.. VerschwindungssĂ€tze fĂŒr analytische Kohomologiegruppen auf komplexen RĂ€umen. Invent. Math. 11 (1970), 263–292.Google Scholar
Greuel, G.-M., Lossen, C. and Shustin, E.. Introduction to singularities and deformations. Springer Monographs in Mathematics, Springer-Verlag, 2007.Google Scholar
Griffiths, P. and Harris, J.. Principles of algebraic geometry. Reprint of the 1978 original. Wiley Classics Library, John Wiley & Sons, Inc., 1994.Google Scholar
Grinenko, M. M.. Birational properties of pencils of del Pezzo surfaces of degrees 1 and 2. Mat. Sb. 191 (2000), 17–38; translation in Sb. Math. 191 (2000), 633– 653.Google Scholar
Grinenko, M. M.. On fibrations into del Pezzo surfaces. Mat. Zametki 69 (2001), 550–565; translation in Math. Notes 69 (2001), 499–513.Google Scholar
Grinenko, M. M.. On fibrewise modifications of fibrings into del Pezzo surfaces of degree 2. Uspekhi Mat. Nauk 56 (2001), 145–146; translation in Russian Math. Surveys 56 (2001), 753–754.Google Scholar
Grinenko, M. M.. Birational properties of pencils of del Pezzo surfaces of degrees 1 and 2. II. Mat. Sb. 194 (2003), 31–60; translation in Sb. Math. 194 (2003), 669–696.Google Scholar
Grothendieck, A.. Sur la classification des fibrĂ©s holomorphes sur la sphĂšre de Riemann. Am. J. Math. 79 (1957), 121–138.Google Scholar
Grothendieck, A.. ElĂ©ments de gĂ©omĂ©trie algĂ©brique. Publ. Math. Inst. Hautes Études Sci. 4 (1960), 8 (1961), 11 (1961), 17 (1963), 20 (1964), 24 (1965), 28 (1966), 32 (1967).Google Scholar
Grothendieck, A.. Cohomologie locale des faisceaux cohĂ©rents et thĂ©orĂšmes de Lefschetz locaux et globaux (SGA 2). AugmentĂ© d’un exposĂ© par M. Raynaud. Advanced Studies in Pure Mathematics 2, North-Holland Publishing Co.; Masson & Cie, Éditeur, 1968.Google Scholar
Grothendieck, A.. Le groupe de Brauer I, II, III. Dix exposĂ©s sur la cohomologie des schĂ©mas, 46–66, 67–87, 88–188. Adv. Stud. Pure Math. 3, North-Holland, 1968.Google Scholar
Grothendieck, A.. RevĂȘtements Ă©tales et groupe fondamental (SGA 1). AugmentĂ© de deux exposĂ©s de M. Raynaud. Lecture Notes in Mathematics 224, Springer-Verlag, 1971.Google Scholar
Grothendieck, A. and Dieudonné, J. A.. Eléments de géométrie algébrique I. Grundlehren der mathematischen Wissenschaften 166, Springer-Verlag, 1971.Google Scholar
Gushel’, N. P.. On Fano varieties of genus 6. Izv. Akad. Nauk SSSR Ser. Mat. 46 (1982), 1159–1174; translation in Math. USSR-Izv. 21 (1983), 445–459.Google Scholar
Gushel’, N. P.. Fano varieties of genus 8. Uspekhi Mat. Nauk 38 (1983), 163–164; translation in Russian Math. Surveys 38 (1983), 192–193.Google Scholar
Hacking, P. and Prokhorov, Y.. Smoothable del Pezzo surfaces with quotient singularities. Compos. Math. 146 (2010), 169–192.Google Scholar
Hacking, P., Tevelev, J. and UrzĂșa, G.. Flipping surfaces. J. Algebraic Geom. 26 (2017), 279–345.Google Scholar
Hacon, C. D. and Kovåcs, S. J.. Classification of higher dimensional algebraic varieties. Oberwolfach Seminars 41, BirkhÀuser Verlag, 2010.Google Scholar
Hacon, C. D. and McKernan, J.. Boundedness of pluricanonical maps of varieties of general type. Invent. Math. 166 (2006), 1–25.Google Scholar
Hacon, C. D. and McKernan, J.. Extension theorems and the existence of flips. Flips for 3-folds and 4-folds, 76–110. Oxford Lecture Ser. Math. Appl. 35, Oxford University Press, 2007.Google Scholar
Hacon, C. D. and McKernan, J.. Existence of minimal models for varieties of log general type II. J. Am. Math. Soc. 23 (2010), 469–490.Google Scholar
Hacon, C. D. and McKernan, J.. The Sarkisov program. J. Algebraic Geom. 22 (2013), 389–405.Google Scholar
Hacon, C. D., McKernan, J. and Xu, C.. ACC for log canonical thresholds. Ann. Math. (2) 180 (2014), 523–571.Google Scholar
Hacon, C. D. and Xu, C.. Existence of log canonical closures. Invent. Math. 192 (2013), 161–195.Google Scholar
Hacon, C. D. and Xu, C.. Boundedness of log Calabi–Yau pairs of Fano type. Math. Res. Lett. 22 (2015), 1699–1716.Google Scholar
Hartshorne, R.. Residues and duality. With an appendix by Deligne, P.. Lecture Notes in Mathematics 20, Springer-Verlag, 1966.Google Scholar
Hartshorne, R.. Algebraic geometry. Graduate Texts in Mathematics 52, Springer-Verlag, 1977.Google Scholar
Hartshorne, R.. Stable reflexive sheaves. Math. Ann. 254 (1980), 121–176.Google Scholar
Hassett, B., Pirutka, A. and Tschinkel, Y.. Stable rationality of quadric surface bundles over surfaces. Acta Math. 220 (2018), 341–365.Google Scholar
Hayakawa, T.. Blowing ups of 3-dimensional terminal singularities. Publ. Res. Inst. Math. Sci. 35 (1999), 515–570.Google Scholar
Hayakawa, T.. Blowing ups of 3-dimensional terminal singularities, II. Publ. Res. Inst. Math. Sci. 36 (2000), 423–456.Google Scholar
Hayakawa, T.. Divisorial contractions to 3-dimensional terminal singularities with discrepancy one. J. Math. Soc. Jpn. 57 (2005), 651–668.Google Scholar
Hayakawa, T. and Takeuchi, K.. On canonical singularities of dimension three. Jpn. J. Math. 13 (1987), 1–46.Google Scholar
Hidaka, F. and Watanabe, K.-i.. Normal Gorenstein surfaces with ample anticanonical divisor. Tokyo J. Math. 4 (1981), 319–330.Google Scholar
Hironaka, H.. On the theory of birational blowing-up. PhD thesis, Harvard University, 1960.Google Scholar
Hironaka, H.. Resolution of singularities of an algebraic variety over a field of characteristic zero: I, II. Ann. Math. (2) 79 (1964), 109–203, 205–326.Google Scholar
Hironaka, H. and Rossi, H.. On the equivalence of imbeddings of exceptional complex spaces. Math. Ann. 156 (1964), 313–333.Google Scholar
Hirzebruch, F.. Topological methods in algebraic geometry. Translated from the German and Appendix One by Schwarzenberger, R. L. E.. Appendix Two by A. Borel. Reprint of the 1978 edition. Classics in Mathematics, Springer-Verlag, 1995.Google Scholar
Holmann, H.. Quotienten komplexer RĂ€ume. Math. Ann. 142 (1961), 407–440.Google Scholar
Holmann, H.. Komplexe RĂ€ume mit komplexen Transformationsgruppen. Math. Ann. 150 (1963), 327–360.Google Scholar
Hudson, H. P.. Cremona transformations in plane and space. Cambridge University Press, 1927.Google Scholar
Huybrechts, D.. Lectures on K3 surfaces. Cambridge Studies in Advanced Mathematics 158, Cambridge University Press, 2016.Google Scholar
Huybrechts, D. and Lehn, M.. The geometry of moduli spaces of sheaves. Second edition. Cambridge Mathematical Library, Cambridge University Press, 2010.Google Scholar
Iano-Fletcher, A. R.. Working with weighted complete intersections. Explicit birational geometry of 3-folds, 101–173. London Math. Soc. Lecture Note Ser. 281, Cambridge University Press, 2000.Google Scholar
Iitaka, S.. Algebraic geometry. An introduction to birational geometry of algebraic varieties. Graduate Texts in Mathematics 76, Springer-Verlag, 1982.Google Scholar
Ishida, M.-N. and Iwashita, N.. Canonical cyclic quotient singularities of dimension three. Complex analytic singularities, 135–151. Adv. Stud. Pure Math. 8, North-Holland, 1987.Google Scholar
Ishii, S.. Introduction to singularities. Second edition. Springer, 2018.Google Scholar
Iskovskih, V. A.. Rational surfaces with a pencil of rational curves. Mat. Sb. 74(116) (1967), 608–638; translation in Math. USSR-Sb. 3 (1967), 563–587.Google Scholar
Iskovskih, V. A.. Rational surfaces with a pencil of rational curves and with positive square of the canonical class. Mat. Sb. 83(125) (1970), 90–119; translation in Math. USSR-Sb. 12 (1970), 91–117.Google Scholar
Iskovskih, V. A.. Birational properties of a surface of degree 4 in P4 . Mat. Sb.88(130) (1972), 31–37; translation in Math. USSR-Sb. 17 (1972), 30–36.Google Scholar
Iskovskih, V. A.. Fano 3-folds. I. Izv. Akad. Nauk SSSR Ser. Mat. 41 (1977), 516–562; translation in Math. USSR-Izv. 11 (1977), 485–527.Google Scholar
Iskovskih, V. A.. Fano 3-folds. II. Izv. Akad. Nauk SSSR Ser. Mat. 42 (1978), 506–549; translation in Math. USSR-Izv. 12 (1978), 469–506.Google Scholar
Iskovskikh, V. A.. Anticanonical models of three-dimensional algebraic varieties. Current problems in mathematics. Vol. 12, 59–157. VINITI, 1979; translation in J. Soviet Math. 13 (1980), 745–814.Google Scholar
Iskovskih, V. A.. Minimal models of rational surfaces over arbitrary fields. Izv. Akad. Nauk SSSR Ser. Mat. 43 (1979), 19–43; translation in Math. USSR-Izv. 14 (1980), 17–39.Google Scholar
Iskovskikh, V. A.. On the rationality problem for conic bundles. Duke Math. J. 54 (1987), 271–294.Google Scholar
Iskovskikh, V. A.. Double projection from a line on Fano threefolds of the first kind. Mat. Sb. 180 (1989), 260–278; translation in Math. USSR-Sb. 66 (1990), 265–284.Google Scholar
Iskovskikh, V. A.. On the rationality problem for conic bundles. Mat. Sb. 182 (1991), 114–121; translation in Math. USSR-Sb. 72 (1992), 105–111.Google Scholar
Iskovskikh, V. A.. A rationality criterion for conic bundles. Mat. Sb. 187 (1996), 75–92; translation in Sb. Math. 187 (1996), 1021–1038.Google Scholar
Iskovskikh, V. A.. Factorization of birational maps of rational surfaces from the viewpoint of Mori theory. Uspekhi Mat. Nauk 51 (1996), 3–72; translation in Russian Math. Surveys 51 (1996), 585–652.Google Scholar
Iskovskih, V. A. and Manin, J. I.. Three-dimensional quartics and counterexamples to the LĂŒroth problem. Mat. Sb. 86(128) (1971), 140–166; translation in Math. USSR-Sb. 15 (1971), 141–166.Google Scholar
Iskovskikh, V. A. and Prokhorov, Y. G.. Fano varieties. Algebraic geometry V, 1–247. Encyclopaedia Math. Sci. 47, Springer, 1999.Google Scholar
Ito, T.. Birational smooth minimal models have equal Hodge numbers in all dimensions. Calabi–Yau varieties and mirror symmetry, 183–194. Fields Inst. Commun. 38, Am. Math. Soc., 2003.Google Scholar
Ito, Y. and Nakamura, I.. Hilbert schemes and simple singularities. New trends in algebraic geometry, 151–233. London Math. Soc. Lecture Note Ser. 264, Cambridge University Press, 1999.Google Scholar
Iwasawa, K.. Lectures on 𝑝-adic 𝐿-functions. Annals of Mathematics Studies 74, Princeton University Press; University of Tokyo Press, 1972.CrossRefGoogle Scholar
Jaffe, D. B.. Local geometry of smooth curves passing through rational double points. Math. Ann. 294 (1992), 645–660.Google Scholar
Jahnke, P. and Radloff, I.. Gorenstein Fano threefolds with base points in the anticanonical system. Compos. Math. 142 (2006), 422–432.Google Scholar
Kajiura, H., Saito, K. and Takahashi, A.. Matrix factorization and representations of quivers II: Type ADE case. Adv. Math. 211 (2007), 327–362.Google Scholar
Kaloghiros, A.-S.. Relations in the Sarkisov program. Compos. Math. 149 (2013), 1685–1709.Google Scholar
Kaup, B.. Äquivalenzrelationen auf allgemeinen komplexen RĂ€umen. Schr. Math. Inst. Univ. MĂŒnster 39, 1968.Google Scholar
Kawakita, M.. Divisorial contractions in dimension three which contract divisors to smooth points. Invent. Math. 145 (2001), 105–119.Google Scholar
Kawakita, M.. Divisorial contractions in dimension three which contract divisors to compound 𝐮1 points. Compos. Math. 133 (2002), 95–116.Google Scholar
Kawakita, M.. General elephants of three-fold divisorial contractions. J. Am. Math. Soc. 16 (2003), 331–362.Google Scholar
Kawakita, M.. Three-fold divisorial contractions to singularities of higher indices. Duke Math. J. 130 (2005), 57–126.Google Scholar
Kawakita, M.. Inversion of adjunction on log canonicity. Invent. Math. 167 (2007), 129–133.Google Scholar
Kawakita, M.. Towards boundedness of minimal log discrepancies by the Riemann–Roch theorem. Am. J. Math. 133 (2011), 1299–1311.Google Scholar
Kawakita, M.. Supplement to classification of threefold divisorial contractions. Nagoya Math. J. 206 (2012), 67–73.Google Scholar
Kawakita, M.. The index of a threefold canonical singularity. Am. J. Math. 137 (2015), 271–280.Google Scholar
Kawakita, M.. Divisors computing the minimal log discrepancy on a smooth surface. Math. Proc. Camb. Philos. Soc. 163 (2017), 187–192.Google Scholar
Kawamata, Y.. A generalization of Kodaira–Ramanujam’s vanishing theorem. Math. Ann. 261 (1982), 43–46.Google Scholar
Kawamata, Y.. Kodaira dimension of algebraic fiber spaces over curves. Invent. Math. 66 (1982), 57–71.Google Scholar
Kawamata, Y.. The cone of curves of algebraic varieties. Ann. Math. (2) 119 (1984), 603–633.Google Scholar
Kawamata, Y.. Minimal models and the Kodaira dimension of algebraic fiber spaces. J. Reine Angew. Math. 363 (1985), 1–46.Google Scholar
Kawamata, Y.. Pluricanonical systems on minimal algebraic varieties. Invent. Math. 79 (1985), 567–588.Google Scholar
Kawamata, Y.. On the plurigenera of minimal algebraic 3-folds with đŸ 0. Math. Ann. 275 (1986), 539–546.Google Scholar
Kawamata, Y.. Crepant blowing-up of 3-dimensional canonical singularities and its application to degenerations of surfaces. Ann. Math. (2) 127 (1988), 93–163.Google Scholar
Kawamata, Y.. On the length of an extremal rational curve. Invent. Math. 105 (1991), 609–611.Google Scholar
Kawamata, Y.. Abundance theorem for minimal threefolds. Invent. Math. 108 (1992), 229–246.Google Scholar
Kawamata, Y.. Boundedness of Q-Fano threefolds. Proceedings of the International Conference on Algebra, 439–445. Contemp. Math. 131, Part 3, Am. Math. Soc., 1992.Google Scholar
Kawamata, Y.. Termination of log flips for algebraic 3-folds. Int. J. Math. 3 (1992), 653–659.Google Scholar
Kawamata, Y.. Divisorial contractions to 3-dimensional terminal quotient singularities. Higher dimensional complex varieties, 241–246. De Gruyter, 1996.Google Scholar
Kawamata, Y.. On Fujita’s freeness conjecture for 3-folds and 4-folds. Math. Ann. 308 (1997), 491–505.Google Scholar
Kawamata, Y.. On the cone of divisors of Calabi–Yau fiber spaces. Int. J. Math. 8 (1997), 665–687.Google Scholar
Kawamata, Y.. Subadjunction of log canonical divisors, II. Am. J. Math. 120 (1998), 893–899.Google Scholar
Kawamata, Y.. On effective non-vanishing and base-point-freeness. Asian J. Math. 4 (2000), 173–181.Google Scholar
Kawamata, Y.. Flops connect minimal models. Publ. Res. Inst. Math. Sci. 44 (2008), 419–423.Google Scholar
Kawamata, Y.. On the abundance theorem in the case of numerical Kodaira dimension zero. Am. J. Math. 135 (2013), 115–124.Google Scholar
Kawamata, Y.. Higher dimensional algebraic varieties. Iwanami Shoten, 2014.Google Scholar
Kawamata, Y., Matsuda, K. and Matsuki, K.. Introduction to the minimal model problem. Algebraic geometry, Sendai, 1985, 283–360. Adv. Stud. Pure Math. 10, North-Holland, 1987.Google Scholar
Keel, S., Matsuki, K. and McKernan, J.. Log abundance theorem for threefolds. Duke Math. J. 75 (1994), 99–119; corrections ibid. 122 (2004), 625–630.Google Scholar
Kempf, G., Knudsen, F., Mumford, D. and Saint-Donat, B.. Toroidal embeddings I. Lecture Notes in Mathematics 339, Springer-Verlag, 1973.Google Scholar
Kiehl, R.. Äquivalenzrelationen in analytischen RĂ€umen. Math. Z. 105 (1968), 1–20.Google Scholar
Kim, I.-K., Okada, T. and Won, J.. K-stability of birationally superrigid Fano 3-fold weighted hypersurfaces. arXiv:2011.07512.Google Scholar
Kleiman, S. L.. Toward a numerical theory of ampleness. Ann. Math. (2) 84 (1966), 293–344.Google Scholar
Klein, F.. Vorlesungen ĂŒber das Ikosaeder und die Auflösung der Gleichungen vom fĂŒnften Grade. Reprint of the 1884 original. BirkhĂ€user Verlag; B. G. Teubner, 1993.Google Scholar
Kobayashi, T.. Lie Group and Representation Theory. To appear from Springer.Google Scholar
Kodaira, K.. On a differential-geometric method in the theory of analytic stacks. Proc. Nat. Acad. Sci. USA 39 (1953), 1268–1273.Google Scholar
Kodaira, K.. On compact analytic surfaces, I, II, III. Ann. Math. (2) 71 (1960), 111–152, 77 (1963), 563–626, 78 (1963), 1–40.Google Scholar
Kollár, J.. The cone theorem: Note to a paper of Y. Kawamata [232]. Ann. Math. (2) 120 (1984), 1–5.Google Scholar
Kollár, J.. Higher direct images of dualizing sheaves I. Ann. Math. (2) 123 (1986), 11–42.Google Scholar
Kollár, J.. Subadditivity of the Kodaira dimension: Fibers of general type. Algebraic geometry, Sendai, 1985, 361–398. Adv. Stud. Pure Math. 10, North-Holland, 1987.Google Scholar
Kollár, J.. Flops. Nagoya Math. J. 113 (1989), 15–36.Google Scholar
Kollár, J.. Flips, flops, minimal models, etc. Surveys in differential geometry, 113–199. Lehigh Univ., 1991.Google Scholar
Kollår, J., ed. Flips and abundance for algebraic threefolds. Astérisque 211, Société Mathématique de France, 1992.Google Scholar
Kollár, J.. Nonrational hypersurfaces. J. Am. Math. Soc. 8 (1995), 241–249.Google Scholar
KollĂĄr, J.. Rational curves on algebraic varieties. Ergebnisse der Mathematik und ihrer Grenzgebiete (3) 32, Springer-Verlag, 1996.Google Scholar
Kollár, J.. Polynomials with integral coefficients, equivalent to a given polynomial. Electron. Res. Announc. Am. Math. Soc. 3 (1997), 17–27.Google Scholar
Kollár, J.. Real algebraic threefolds, III. Conic bundles. J. Math. Sci. (N.Y.) 94 (1999), 996–1020.Google Scholar
KollĂĄr, J.. Singularities of the minimal model program. With the collaboration of KovĂĄcs, S.. Cambridge Tracts in Mathematics 200, Cambridge University Press, 2013.Google Scholar
Kollár, J. and Kovács, S. J.. Log canonical singularities are Du Bois. J. Am. Math. Soc. 23 (2010), 791–813.Google Scholar
Kollár, J. and Matsusaka, T.. Riemann–Roch type inequalities. Am. J. Math. 105 (1983), 229–252.Google Scholar
Kollár, J., Miyaoka, Y. and Mori, S.. Rational curves on Fano varieties. Classification of irregular varieties, 100–105. Lecture Notes in Math. 1515, Springer, 1992.Google Scholar
Kollár, J., Miyaoka, Y. and Mori, S.. Rationally connected varieties. J. Algebraic Geom. 1 (1992), 429–448.Google Scholar
Kollár, J., Miyaoka, Y. and Mori, S.. Rational connectedness and boundedness of Fano manifolds. J. Differ. Geom. 36 (1992), 765–779.Google Scholar
Kollár, J., Miyaoka, Y., Mori, S. and Takagi, H.. Boundedness of canonical Q-Fano 3-folds. Proc. Jpn. Acad. Ser. A Math. Sci. 76 (2000), 73–77.Google Scholar
Kollár, J. and Mori, S.. Classification of three-dimensional flips. J. Am. Math. Soc. 5 (1992), 533–703; errata by S. Mori ibid. 20 (2007), 269–271.Google Scholar
KollĂĄr, J. and Mori, S.. Birational geometry of algebraic varieties. With the collaboration of Clemens, C. H. and Corti, A.. Translated from the 1998 Japanese original. Cambridge Tracts in Mathematics 134, Cambridge University Press, 1998.Google Scholar
Kollár, J. and Shepherd-Barron, N. I.. Threefolds and deformations of surface singularities. Invent. Math. 91 (1988), 299–338.Google Scholar
Kontsevich, M.. Lecture at Orsay, 7 December 1995.Google Scholar
Kontsevich, M. and Tschinkel, Y.. Specialization of birational types. Invent. Math. 217 (2019), 415–432.Google Scholar
Kustin, A. R. and Miller, M.. Constructing big Gorenstein ideals from small ones. J. Algebra 85 (1983), 303–322.Google Scholar
Lai, C.-J.. Varieties fibered by good minimal models. Math. Ann. 350 (2011), 533–547.Google Scholar
Lang, S.. Algebra. Revised third edition. Graduate Texts in Mathematics 211, Springer-Verlag, 2002.Google Scholar
Lange, C.. When is the underlying space of an orbifold a manifold? Trans. Am. Math. Soc. 372 (2019), 2799–2828.Google Scholar
Langer, A.. Semistable sheaves in positive characteristic. Ann. Math. (2) 159 (2004), 251–276; addendum ibid. 160 (2004), 1211–1213.Google Scholar
Laufer, H. B.. Taut two-dimensional singularities. Math. Ann. 205 (1973), 131–164.Google Scholar
Laufer, H. B.. On minimally elliptic singularities. Am. J. Math. 99 (1977), 1257–1295.Google Scholar
Lazarsfeld, R.. Positivity in algebraic geometry I. Ergebnisse der Mathematik und ihrer Grenzgebiete (3) 48, Springer-Verlag, 2004.Google Scholar
Lazarsfeld, R. and Mustaƣă, M.. Convex bodies associated to linear series. Ann. Sci. Éc. Norm. SupĂ©r. (4) 42 (2009), 783–835.Google Scholar
Levine, M. N.. Deformations of uni-ruled varieties. Duke Math. J. 48 (1981), 467–473.Google Scholar
Levine, M.. Some examples from the deformation theory of ruled varieties. Am. J. Math. 103 (1981), 997–1020.Google Scholar
Li, C.. K-semistability is equivariant volume minimization. Duke Math. J. 166 (2017), 3147–3218.Google Scholar
Li, C.. đș-uniform stability and KĂ€hler–Einstein metrics on Fano varieties. Invent. Math. 227 (2022), 661–744.Google Scholar
Lin, J.. Birational unboundedness of Q-Fano threefolds. Int. Math. Res. Not. IMRN 2003 (2003), 301–312.Google Scholar
Lipman, J.. Rational singularities, with applications to algebraic surfaces and unique factorization. Publ. Math. Inst. Hautes Études Sci. 36 (1969), 195–279.Google Scholar
Liu, Y., Xu, C. and Zhuang, Z.. Finite generation for valuations computing stability thresholds and applications to K-stability. Ann. Math. (2) 196 (2022), 507–566.Google Scholar
Lojasiewicz, S.. Triangulation of semi-analytic sets. Ann. Sc. Norm. Super. Pisa Cl. Sci. (3) 18 (1964), 449–474.Google Scholar
Maclagan, D.. Antichains of monomial ideals are finite. Proc. Am. Math. Soc. 129 (2001), 1609–1615.Google Scholar
Mal’cev, A. I.. On the faithful representation of infinite groups by matrices. Mat. Sb. 8(50) (1940), 405–422; translation in Am. Math. Soc. Transl. (2) 45 (1965), 1–18.Google Scholar
Manin, J. I.. Rational surfaces over perfect fields. Publ. Math. Inst. Hautes Études Sci. 30 (1966), 55–113.Google Scholar
Manin, J. I.. Rational surfaces over perfect fields. II. Mat. Sb. 72(114) (1967), 161–192; translation in Math. USSR-Sb. 1 (1967), 141–168.Google Scholar
Manin, Y. I.. Cubic forms. Algebra, geometry, arithmetic. Translated from the Russian by Hazewinkel, M.. Second edition. North-Holland Mathematical Library 4, North-Holland Publishing Co., 1986.Google Scholar
Markushevich, D.. Minimal discrepancy for a terminal cDV singularity is 1. J. Math. Sci. Univ. Tokyo 3 (1996), 445–456.Google Scholar
Martinelli, D., Schreieder, S. and Tasin, L.. On the number and boundedness of log minimal models of general type. Ann. Sci. Éc. Norm. SupĂ©r. (4) 53 (2020), 1183–1207.Google Scholar
Masiewicki, L.. Universal properties of Prym varieties with an application to algebraic curves of genus five. Trans. Am. Math. Soc. 222 (1976), 221–240.Google Scholar
Matsuki, K.. Weyl groups and birational transformations among minimal models. Mem. Am. Math. Soc. 116, no 557, (1995).Google Scholar
Matsuki, K.. Introduction to the Mori program. Universitext, Springer-Verlag, 2002.Google Scholar
Matsumura, H.. Commutative ring theory. Translated from the Japanese by Reid, M.. Paperback edition. Cambridge Studies in Advanced Mathematics 8, Cambridge University Press, 1989.Google Scholar
Matsusaka, T.. Algebraic deformations of polarized varieties. Nagoya Math. J. 31 (1968), 185–245; corrections ibid. 33 (1968), 137, 36 (1968), 119.Google Scholar
Matsusaka, T.. Polarized varieties with a given Hilbert polynomial. Am. J. Math. 94 (1972), 1027–1077.Google Scholar
Matsushita, D.. On smooth 4-fold flops. Saitama Math. J. 15 (1997), 47–54.Google Scholar
McKay, J.. Graphs, singularities, and finite groups. The Santa Cruz Conference on Finite Groups, 183–186. Proc. Sympos. Pure Math. 37, Am. Math. Soc., 1980.Google Scholar
Mehta, V. B. and Ramanathan, A.. Semistable sheaves on projective varieties and their restriction to curves. Math. Ann. 258 (1981/82), 213–224.Google Scholar
Mehta, V. B. and Ramanathan, A.. Restriction of stable sheaves and representations of the fundamental group. Invent. Math. 77 (1984), 163–172.Google Scholar
Mella, M.. Birational geometry of quartic 3-folds II: The importance of being Q-factorial. Math. Ann. 330 (2004), 107–126.Google Scholar
Migliore, J. C.. Introduction to liaison theory and deficiency modules. Progress in Mathematics 165, BirkhÀuser Boston, Inc., 1998.Google Scholar
Milne, J. S.. Étale cohomology. Princeton Mathematical Series 33, Princeton University Press, 1980.Google Scholar
Milne, J. S.. Jacobian varieties. Arithmetic geometry, 167–212. Springer, 1986.Google Scholar
Milnor, J.. Morse theory. Annals of Mathematics Studies 51, Princeton University Press, 1963.Google Scholar
Milnor, J.. Singular points of complex hypersurfaces. Annals of Mathematics Studies 61, Princeton University Press; University of Tokyo Press, 1968.Google Scholar
Miyanishi, M.. Algebraic methods in the theory of algebraic threefolds – surrounding the works of Iskovskikh, Mori and Sarkisov. Algebraic varieties and analytic varieties, 69–99. Adv. Stud. Pure Math. 1, North-Holland, 1983.Google Scholar
Miyanishi, M. and Zhang, D. Q.. Gorenstein log del Pezzo surfaces of rank one. J. Algebra 118 (1988), 63–84.Google Scholar
Miyaoka, Y.. Tricanonical maps of numerical Godeaux surfaces. Invent. Math. 34 (1976), 99–111.Google Scholar
Miyaoka, Y.. Deformations of a morphism along a foliation and applications. Algebraic geometry, Bowdoin, 1985, 245–268. Proc. Sympos. Pure Math. 46, Part 1, Am. Math. Soc., 1987.Google Scholar
Miyaoka, Y.. The Chern classes and Kodaira dimension of a minimal variety. Algebraic geometry, Sendai, 1985, 449–476. Adv. Stud. Pure Math. 10, North-Holland, 1987.Google Scholar
Miyaoka, Y.. Abundance conjecture for 3-folds: Case 𝜈 = 1. Compos. Math. 68 (1988), 203–220.Google Scholar
Miyaoka, Y.. On the Kodaira dimension of minimal threefolds. Math. Ann. 281 (1988), 325–332.Google Scholar
Miyaoka, Y. and Mori, S.. A numerical criterion for uniruledness. Ann. Math. (2) 124 (1986), 65–69.Google Scholar
Miyaoka, Y. and Peternell, T.. Geometry of higher dimensional algebraic varieties. DMV Seminar 26, BirkhÀuser Verlag, 1997.Google Scholar
Mo˘ıƥezon, B. G.. Algebraic homology classes on algebraic varieties. Izv. Akad. Nauk SSSR Ser. Mat. 31 (1967), 225–268; translation in Math. USSR-Izv. 1 (1967), 209–251.Google Scholar
Mori, S.. Projective manifolds with ample tangent bundles. Ann. Math. (2) 110 (1979), 593–606.Google Scholar
Mori, S.. Threefolds whose canonical bundles are not numerically effective. Ann. Math. (2) 116 (1982), 133–176.Google Scholar
Mori, S.. On 3-dimensional terminal singularities. Nagoya Math. J. 98 (1985), 43–66.Google Scholar
Mori, S.. Classification of higher-dimensional varieties. Algebraic geometry, Bowdoin, 1985, 269–331. Proc. Sympos. Pure Math. 46, Part 1, Am. Math. Soc., 1987.CrossRefGoogle Scholar
Mori, S.. Flip theorem and the existence of minimal models for 3-folds. J. Am. Math. Soc. 1 (1988), 117–253.Google Scholar
Mori, S.. On semistable extremal neighborhoods. Higher dimensional birational geometry, 157–184. Adv. Stud. Pure Math. 35, Math. Soc. Japan, 2002.Google Scholar
Mori, S. and Mukai, S.. Classification of Fano 3-folds with đ”2 2. Manuscripta Math. 36 (1981), 147–162; erratum ibid. 110 (2003), 407.Google Scholar
Mori, S. and Prokhorov, Y.. On Q-conic bundles. Publ. Res. Inst. Math. Sci. 44 (2008), 315–369.Google Scholar
Mori, S. and Prokhorov, Y.. On Q-conic bundles, II. Publ. Res. Inst. Math. Sci. 44 (2008), 955–971.Google Scholar
Mori, S. and Prokhorov, Y.. On Q-conic bundles, III. Publ. Res. Inst. Math. Sci. 45 (2009), 787–810.Google Scholar
Mori, S. and Prokhorov, Y. G.. Multiple fibers of del Pezzo fibrations. Tr. Mat. Inst. Steklova 264 (2009), 137–151; reprinted in Proc. Steklov Inst. Math. 264 (2009), 131–145.Google Scholar
Mori, S. and Prokhorov, Y.. Threefold extremal contractions of type (IA). Kyoto J. Math. 51 (2011), 393–438.Google Scholar
Mori, S. and Prokhorov, Y.. 3-fold extremal contractions of types (IC) and (IIB). Proc. Edinb. Math. Soc. (2) 57 (2014), 231–252.Google Scholar
Mori, S. and Prokhorov, Y. G.. Threefold extremal contractions of type (IIA). I. Izv. Ross. Akad. Nauk Ser. Mat. 80 (2016), 77–102; reprinted in Izv. Math. 80 (2016), 884–909.Google Scholar
Mori, S. and Prokhorov, Y.. Threefold extremal contractions of type (IIA). Part II. Geometry and physics. Vol. II, 623–652. Oxford University Press, 2018.Google Scholar
Morrison, D. R.. Canonical quotient singularities in dimension three. Proc. Am. Math. Soc. 93 (1985), 393–396.Google Scholar
Morrison, D. R.. Compactifications of moduli spaces inspired by mirror symmetry. JournĂ©es de gĂ©omĂ©trie algĂ©brique d’Orsay. AstĂ©risque 218 (1993), 243–271.Google Scholar
Morrison, D. R.. Beyond the KĂ€hler cone. Proceedings of the Hirzebruch 65 Conference on Algebraic Geometry, 361–376. Israel Math. Conf. Proc. 9, Bar-Ilan Univ., 1996.Google Scholar
Morrison, D. R. and Stevens, G.. Terminal quotient singularities in dimensions three and four. Proc. Am. Math. Soc. 90 (1984), 15–20.Google Scholar
Mukai, S.. On the moduli space of bundles on K3 surfaces, I. Vector bundles on algebraic varieties, 341–413. Tata Inst. Fund. Res. Stud. Math. 11, Tata Inst. Fund. Res., 1987.Google Scholar
Mukai, S.. Curves, K3 surfaces and Fano 3-folds of genus 10. Algebraic geometry and commutative algebra. Vol. I, 357–377. Kinokuniya, 1988.Google Scholar
Mukai, S.. Biregular classification of Fano 3-folds and Fano manifolds of coindex 3. Proc. Nat. Acad. Sci. USA 86 (1989), 3000–3002.Google Scholar
Mukai, S.. Fano 3-folds. Complex projective geometry, 255–263. London Math. Soc. Lecture Note Ser. 179, Cambridge University Press, 1992.Google Scholar
Mukai, S.. Curves and Grassmannians. Algebraic geometry and related topics, 19–40. Conf. Proc. Lecture Notes Algebraic Geom. I, Int. Press, 1993.Google Scholar
Mukai, S.. Curves and symmetric spaces, I. Am. J. Math. 117 (1995), 1627–1644.Google Scholar
Mukai, S.. New developments in the theory of Fano threefolds: Vector bundle method and moduli problems. Sugaku Expositions 15 (2002), 125–150.Google Scholar
Mukai, S.. An introduction to invariants and moduli. Translated from the 1998 and 2000 Japanese editions by Oxbury, W. M.. Cambridge Studies in Advanced Mathematics 81, Cambridge University Press, 2003.Google Scholar
Mukai, S.. Curves and symmetric spaces, II. Ann. Math. (2) 172 (2010), 1539–1558.Google Scholar
Mukai, S. and Umemura, H.. Minimal rational threefolds. Algebraic geometry, 490–518. Lecture Notes in Math. 1016, Springer, 1983.Google Scholar
Mumford, D.. The topology of normal singularities of an algebraic surface and a criterion for simplicity. Publ. Math. Inst. Hautes Études Sci. 9 (1961), 5–22.Google Scholar
Mumford, D.. Abelian varieties. Tata Institute of Fundamental Research Studies in Mathematics 5, Oxford University Press, 1970.Google Scholar
Mumford, D.. Theta characteristics of an algebraic curve. Ann. Sci. Éc. Norm. SupĂ©r. (4) 4 (1971), 181–192.Google Scholar
Mumford, D.. Prym varieties I. Contributions to analysis, 325–350. Academic Press, 1974.Google Scholar
Mumford, D., Fogarty, J. and Kirwan, F.. Geometric invariant theory. Third edition. Ergebnisse der Mathematik und ihrer Grenzgebiete (2) 34, Springer-Verlag, 1994.Google Scholar
Mustaƣă, M. and Nakamura, Y.. A boundedness conjecture for minimal log discrepancies on a fixed germ. Local and global methods in algebraic geometry, 287–306. Contemp. Math. 712, Am. Math. Soc., 2018.Google Scholar
Nagata, M.. On rational surfaces, II. Mem. Coll. Sci. Univ. Kyoto Ser. A Math. 33 (1960/61), 271–293.Google Scholar
Nakayama, N.. Invariance of the plurigenera of algebraic varieties under minimal model conjectures. Topology 25 (1986), 237–251.Google Scholar
Nakayama, N.. The lower semi-continuity of the plurigenera of complex varieties. Algebraic geometry, Sendai, 1985, 551–590. Adv. Stud. Pure Math. 10, North-Holland, 1987.Google Scholar
Nakayama, N.. Zariski-decomposition and abundance. MSJ Memoirs 14, Mathematical Society of Japan, 2004.Google Scholar
Namikawa, Y.. Smoothing Fano 3-folds. J. Algebraic Geom. 6 (1997), 307–324.Google Scholar
Namikawa, Y.. Periods of Enriques surfaces. Math. Ann. 270 (1985), 201–222.Google Scholar
Nicaise, J. and Shinder, E.. The motivic nearby fiber and degeneration of stable rationality. Invent. Math. 217 (2019), 377–413.Google Scholar
Oda, T.. Convex bodies and algebraic geometry. Translated from the Japanese. Ergebnisse der Mathematik und ihrer Grenzgebiete (3) 15, Springer-Verlag, 1988.Google Scholar
Odaka, Y. and Sano, Y.. Alpha invariant and K-stability of Q-Fano varieties. Adv. Math. 229 (2012), 2818–2834.Google Scholar
Okada, T.. On the birational unboundedness of higher dimensional Q-Fano varieties. Math. Ann. 345 (2009), 195–212.Google Scholar
Okada, T.. On birational rigidity of singular del Pezzo fibrations of degree 1. J. Lond. Math. Soc. (2) 102 (2020), 1–21.Google Scholar
Okonek, C., Schneider, M. and Spindler, H.. Vector bundles on complex projective spaces. Corrected reprint of the 1988 edition. With an appendix by Gelfand, S. I.. Modern BirkhÀuser Classics, BirkhÀuser/Springer Basel AG, 2011.Google Scholar
Pan, I.. Une remarque sur la gĂ©nĂ©ration du groupe de Cremona. Bol. Soc. Brasil. Mat. (N.S.) 30 (1999), 95–98.Google Scholar
Panin, I. A.. Rationality of bundles of conics with degenerate curve of degree five and even theta-characteristic. Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 103 (1980), 100–105; translation in J. Soviet Math. 24 (1984), 449–452.Google Scholar
Papadakis, S. A. and Reid, M.. Kustin–Miller unprojection without complexes. J. Algebraic Geom. 13 (2004), 563–577.Google Scholar
Park, J.. Birational maps of del Pezzo fibrations. J. Reine Angew. Math. 538 (2001), 213–221.Google Scholar
Pjatecki˘ı-Ć apiro, I. I. and Ć afarevič, I. R.. A Torelli theorem for algebraic surfaces of type K3. Izv. Akad. Nauk SSSR Ser. Mat. 35 (1971), 530–572; translation in Math. USSR-Izv. 5 (1971), 547–588.Google Scholar
Pourcin, G.. ThĂ©orĂšme de Douady au-dessus de 𝑆. Ann. Sc. Norm. Super. Pisa Cl. Sci. (3) 23 (1969), 451–459.Google Scholar
Prendergast-Smith, A.. The cone conjecture for abelian varieties. J. Math. Sci. Univ. Tokyo 19 (2012), 243–261.Google Scholar
Prokhorov, Y. G.. On the existence of complements of the canonical divisor for Mori conic bundles. Mat. Sb. 188 (1997), 99–120; translation in Sb. Math. 188 (1997), 1665–1685.Google Scholar
Prokhorov, Y. G.. On the degree of Fano threefolds with canonical Gorenstein singularities. Mat. Sb. 196 (2005), 81–122; translation in Sb. Math. 196 (2005), 77–114.Google Scholar
Prokhorov, Y. G.. The degree of Q-Fano threefolds. Mat. Sb. 198 (2007), 153–174; translation in Sb. Math. 198 (2007), 1683–1702.Google Scholar
Prokhorov, Y.. Q-Fano threefolds of large Fano index, I. Doc. Math. 15 (2010), 843–872.Google Scholar
Prokhorov, Y.. A note on degenerations of del Pezzo surfaces. Ann. Inst. Fourier (Grenoble) 65 (2015), 369–388.Google Scholar
Prokhorov, Y.. Log-canonical degenerations of del Pezzo surfaces in Q-Gorenstein families. Kyoto J. Math. 59 (2019), 1041–1073.Google Scholar
Prokhorov, Y. and Reid, M.. On Q-Fano 3-folds of Fano index 2. Minimal models and extremal rays (Kyoto, 2011), 397–420. Adv. Stud. Pure Math. 70, Math. Soc. Japan, 2016.Google Scholar
Pukhlikov, A. V.. Birational automorphisms of algebraic threefolds with a pencil of Del Pezzo surfaces. Izv. Ross. Akad. Nauk Ser. Mat. 62 (1998), 123–164; translation in Izv. Math. 62 (1998), 115–155.Google Scholar
Pukhlikov, A. V.. Birational automorphisms of Fano hypersurfaces. Invent. Math. 134 (1998), 401–426.Google Scholar
Pukhlikov, A. V.. Fiber-wise birational correspondences. Mat. Zametki 68 (2000), 120–130; translation in Math. Notes 68 (2000), 103–112.Google Scholar
Rees, D.. On a problem of Zariski. Illinois J. Math. 2 (1958), 145–149.Google Scholar
Reid, M.. Canonical 3-folds. JournĂ©es de gĂ©ometrie algĂ©brique d’Angers, Juillet 1979, 273–310. Sijthoff & Noordhoff, 1980.Google Scholar
Reid, M.. Lines on Fano 3-folds according to Shokurov. Institut Mittag-Leffler report, no 11, 1980.Google Scholar
Reid, M.. Decomposition of toric morphisms. Arithmetic and geometry. Vol. II, 395–418. Progr. Math. 36, BirkhĂ€user Boston, 1983.Google Scholar
Reid, M.. Minimal models of canonical 3-folds. Algebraic varieties and analytic varieties, 131–180. Adv. Stud. Pure Math. 1, North-Holland, 1983.Google Scholar
Reid, M.. Projective morphisms according to Kawamata. Warwick preprint, 1983.Google Scholar
Reid, M.. Young person’s guide to canonical singularities. Algebraic geometry, Bowdoin, 1985, 345–414. Proc. Sympos. Pure Math. 46, Part 1, Am. Math. Soc., 1987.Google Scholar
Reid, M.. Nonnormal del Pezzo surfaces. Publ. Res. Inst. Math. Sci. 30 (1994), 695–727.Google Scholar
Reid, M.. Chapters on algebraic surfaces. Complex algebraic geometry, 3–159. IAS/Park City Math. Ser. 3, Am. Math. Soc., 1997.Google Scholar
Reider, I.. Vector bundles of rank 2 and linear systems on algebraic surfaces. Ann. Math. (2) 127 (1988), 309–316.Google Scholar
Saint-Donat, B.. Sur les Ă©quations dĂ©finissant une courbe algĂ©brique. C. R. Acad. Sci. Paris SĂ©r. A 274 (1972), 324–327, 487–489.Google Scholar
Saint-Donat, B.. On Petri’s analysis of the linear system of quadrics through a canonical curve. Math. Ann. 206 (1973), 157–175.Google Scholar
Saint-Donat, B.. Projective models of K-3 surfaces. Am. J. Math. 96 (1974), 602–639.Google Scholar
Sano, T.. Deforming elephants of Q-Fano 3-folds. J. Lond. Math. Soc. (2) 95 (2017), 23–51.Google Scholar
Sarkisov, V. G.. Birational automorphisms of conic bundles. Izv. Akad. Nauk SSSR Ser. Mat. 44 (1980), 918–945; translation in Math. USSR-Izv. 17 (1981), 177–202.Google Scholar
Sarkisov, V. G.. On conic bundle structures. Izv. Akad. Nauk SSSR Ser. Mat. 46 (1982), 371–408; translation in Math. USSR-Izv. 20 (1983), 355–390.Google Scholar
Sarkisov, V. G.. Birational maps of standard Q-Fano fiberings. Kurchatov Institute of Atomic Energy preprint, 1989.Google Scholar
Schreieder, S.. Stably irrational hypersurfaces of small slopes. J. Am. Math. Soc. 32 (2019), 1171–1199.Google Scholar
Seifert, H. and Threlfall, W.. A textbook of topology. Translated from the 1934 German edition by Goldman, M. A.. With Topology of 3-dimensional fibered spaces by Seifert, H., translated by Heil, W.. Pure and Applied Mathematics 89, Academic Press, Inc., 1980.Google Scholar
Serre, J.-P.. GĂ©omĂ©trie algĂ©brique et gĂ©omĂ©trie analytique. Ann. Inst. Fourier (Grenoble) 6 (1956), 1–42.Google Scholar
Shephard, G. C. and Todd, J. A.. Finite unitary reflection groups. Canad. J. Math. 6 (1954), 274–304.Google Scholar
Shepherd-Barron, N. I.. Miyaoka’s theorems on the generic seminegativity of 𝑇𝑋 and on the Kodaira dimension of minimal regular threefolds. Flips and abundance for algebraic threefolds, 103–114. AstĂ©risque 211, Soc. Math. France, 1992.Google Scholar
Shepherd-Barron, N. I.. Semi-stability and reduction mod 𝑝. Topology 37 (1998), 659–664.Google Scholar
Shepherd-Barron, N. I.. Stably rational irrational varieties. The Fano Conference, 693–700. Univ. Torino, 2004.Google Scholar
Shin, K.-H.. 3-dimensional Fano varieties with canonical singularities. Tokyo J. Math. 12 (1989), 375–385.Google Scholar
Ơokurov, V. V.. Smoothness of the general anticanonical divisor on a Fano 3-fold. Izv. Akad. Nauk SSSR Ser. Mat. 43 (1979), 430–441; translation in Math. USSR-Izv. 14 (1980), 395–405.Google Scholar
Ơokurov, V. V.. The existence of a straight line on Fano 3-folds. Izv. Akad. Nauk SSSR Ser. Mat. 43 (1979), 922–964; translation in Math. USSR-Izv. 15 (1980), 173–209.Google Scholar
Shokurov, V. V.. Prym varieties: Theory and applications. Izv. Akad. Nauk SSSR Ser. Mat. 47 (1983), 785–855; translation in Math. USSR-Izv. 23 (1984), 83–147.Google Scholar
Shokurov, V. V.. The nonvanishing theorem. Izv. Akad. Nauk SSSR Ser. Mat. 49 (1985), 635–651; translation in Math. USSR-Izv. 26 (1986), 591–604.Google Scholar
Shokurov, V. V.. 3-fold log flips. With an appendix by Kawamata, Y.. Izv. Ross. Akad. Nauk Ser. Mat. 56 (1992), 105–203; translation in Izv. Math. 40 (1993), 95–202.Google Scholar
Shokurov, V. V.. 3-fold log models. J. Math. Sci. (N.Y.) 81 (1996), 2667–2699.Google Scholar
Shokurov, V. V.. Prelimiting flips. Tr. Mat. Inst. Steklova 240 (2003), 82–219; reprinted in Proc. Steklov Inst. Math. 240 (2003), 75–213.Google Scholar
Shokurov, V. V.. Letters of a bi-rationalist V: Mld’s and termination of log flips. Tr. Mat. Inst. Steklova 246 (2004), 328–351; translation in Proc. Steklov Inst. Math. 246 (2004), 315–336.Google Scholar
Shramov, K. A.. On the rationality of non-singular threefolds with a pencil of Del Pezzo surfaces of degree 4. Mat. Sb. 197 (2006), 133–144; translation in Sb. Math. 197 (2006), 127–137.Google Scholar
Silverman, J. H.. The arithmetic of elliptic curves. Second edition. Graduate Texts in Mathematics 106, Springer, 2009.Google Scholar
Spanier, E. H.. Algebraic topology. Corrected reprint of the 1966 original. Springer-Verlag, 1995.Google Scholar
Springer, T. A.. Invariant theory. Lecture Notes in Mathematics 585, Springer-Verlag, 1977.Google Scholar
Stepanov, D. A.. Smooth three-dimensional canonical thresholds. Mat. Zametki 90 (2011), 285–299; translation in Math. Notes 90 (2011), 265–278.Google Scholar
Sterk, H.. Finiteness results for algebraic K3 surfaces. Math. Z. 189 (1985), 507–513.Google Scholar
Stibitz, C. and Zhuang, Z.. K-stability of birationally superrigid Fano varieties. Compos. Math. 155 (2019), 1845–1852.Google Scholar
Suzuki, K.. On Fano indices of Q-Fano 3-folds. Manuscripta Math. 114 (2004), 229–246.Google Scholar
Swinnerton-Dyer, H. P. F.. Rational points on del Pezzo surfaces of degree 5. Algebraic geometry, Oslo 1970, 287–290. Wolters-Noordhoff, 1972.Google Scholar
Szabó, E.. Divisorial log terminal singularities. J. Math. Sci. Univ. Tokyo 1 (1994), 631–639.Google Scholar
Takayama, S.. Pluricanonical systems on algebraic varieties of general type. Invent. Math. 165 (2006), 551–587.Google Scholar
Takeuchi, K.. Some birational maps of Fano 3-folds. Compos. Math. 71 (1989), 265–283.Google Scholar
Tennison, B. R.. Sheaf theory. London Mathematical Society Lecture Note Series 20, Cambridge University Press, 1975.Google Scholar
Tian, G.. On KĂ€hler–Einstein metrics on certain KĂ€hler manifolds with C1 (M) > 0. Invent. Math. 89 (1987), 225–246.Google Scholar
Tian, G.. KĂ€hler–Einstein metrics with positive scalar curvature. Invent. Math. 130 (1997), 1–37.Google Scholar
Tian, G.. K-stability and KĂ€hler–Einstein metrics. Comm. Pure Appl. Math. 68 (2015), 1085–1156; corrigendum ibid. 68 (2015), 2082–2083.Google Scholar
Totaro, B.. Towards a Schubert calculus for complex reflection groups. Math. Proc. Camb. Philos. Soc. 134 (2003), 83–93.Google Scholar
Totaro, B.. Hilbert’s 14th problem over finite fields and a conjecture on the cone of curves. Compos. Math. 144 (2008), 1176–1198.Google Scholar
Totaro, B.. The cone conjecture for Calabi–Yau pairs in dimension 2. Duke Math. J. 154 (2010), 241–263.Google Scholar
Totaro, B.. Algebraic surfaces and hyperbolic geometry. Current developments in algebraic geometry, 405–426. Math. Sci. Res. Inst. Publ. 59, Cambridge University Press, 2012.Google Scholar
Totaro, B.. Hypersurfaces that are not stably rational. J. Am. Math. Soc. 29 (2016), 883–891.Google Scholar
Tougeron, J.-C.. IdĂ©aux de fonctions diffĂ©rentiables I. Ann. Inst. Fourier (Grenoble) 18 (1968), 177–240.Google Scholar
Tsuji, H.. Pluricanonical systems of projective varieties of general type I. Osaka J. Math. 43 (2006), 967–995.Google Scholar
Tyurin, A. N.. On intersections of quadrics. Uspekhi Mat. Nauk 30 (1975), 51–99; translation in Russian Math. Surveys 30 (1975), 51–105.Google Scholar
Tyurina, G. N.. Resolution of singularities of plane deformations of double rational points. Funktsional. Anal. i Prilozhen. 4 (1970), 77–83; translation in Funct. Anal. Appl. 4 (1970), 68–73.Google Scholar
Tziolas, N.. Terminal 3-fold divisorial contractions of a surface to a curve I. Compos. Math. 139 (2003), 239–261.Google Scholar
Tziolas, N.. Families of đ·-minimal models and applications to 3-fold divisorial contractions. Proc. Lond. Math. Soc. (3) 90 (2005), 345–370; corrigendum ibid. 93 (2006), 82–84.Google Scholar
Tziolas, N.. Three dimensional divisorial extremal neighborhoods. Math. Ann. 333 (2005), 315–354.Google Scholar
Tziolas, N.. Q-Gorenstein deformations of nonnormal surfaces. Am. J. Math. 131 (2009), 171–193.Google Scholar
Tziolas, N.. Three-fold divisorial extremal neighborhoods over c𝐾7 and c𝐾6 compound DuVal singularities. Int. J. Math. 21 (2010), 1–23.Google Scholar
Ueno, K.. Classification theory of algebraic varieties and compact complex spaces. Notes written in collaboration with Cherenack, P.. Lecture Notes in Mathematics 439, Springer-Verlag, 1975.Google Scholar
Veys, W.. Zeta functions and ‘Kontsevich invariants’ on singular varieties. Canad. J. Math. 53 (2001), 834–865.Google Scholar
Viehweg, E.. Canonical divisors and the additivity of the Kodaira dimension for morphisms of relative dimension one. Compos. Math. 35 (1977), 197–223; correction ibid. 35 (1977), 336.Google Scholar
Viehweg, E.. Klassifikationstheorie algebraischer VarietĂ€ten der Dimension drei. Compos. Math. 41 (1980), 361–400.Google Scholar
Viehweg, E.. Die AdditivitĂ€t der Kodaira Dimension fĂŒr projektive FaserrĂ€ume ĂŒber VarietĂ€ten des allgemeinen Typs. J. Reine Angew. Math. 330 (1982), 132– 142.Google Scholar
Viehweg, E.. Vanishing theorems. J. Reine Angew. Math. 335 (1982), 1–8.Google Scholar
Viehweg, E.. Weak positivity and the additivity of the Kodaira dimension for certain fibre spaces. Algebraic varieties and analytic varieties, 329–353. Adv. Stud. Pure Math. 1, North-Holland, 1983.Google Scholar
Viehweg, E. and Zhang, D.-Q.. Effective Iitaka fibrations. J. Algebraic Geom. 18 (2009), 711–730.Google Scholar
Voisin, C.. Hodge theory and complex algebraic geometry I. Translated from the French by Schneps, L.. Cambridge Studies in Advanced Mathematics 76, Cambridge University Press, 2002.Google Scholar
Voisin, C.. Hodge theory and complex algebraic geometry II. Translated from the French by Schneps, L.. Cambridge Studies in Advanced Mathematics 77, Cambridge University Press, 2003.Google Scholar
Voisin, C.. Unirational threefolds with no universal codimension 2 cycle. Invent. Math. 201 (2015), 207–237.Google Scholar
Wang, C.-L.. On the topology of birational minimal models. J. Differ. Geom. 50 (1998), 129–146.Google Scholar
Wang, C.-L.. Cohomology theory in birational geometry. J. Differ. Geom. 60 (2002), 345–354.Google Scholar
Werner, J.. Kleine Auflösungen spezieller dreidimensionaler VarietÀten. Dissertation, Rheinische Friedrich-Wilhelms-UniversitÀt, 1987.Google Scholar
White, G. K.. Lattice tetrahedra, Canad. J. Math. 16 (1964), 389–396.Google Scholar
Xu, C.. A minimizing valuation is quasi-monomial. Ann. Math. (2) 191 (2020), 1003–1030.Google Scholar
Yamamoto, Y.. Divisorial contractions to cDV points with discrepancy greater than 1. Kyoto J. Math. 58 (2018), 529–567.Google Scholar
Ye, F. and Zhu, Z.. On Fujita’s freeness conjecture in dimension 5. Adv. Math. 371 (2020), 107210, 56pp.Google Scholar
Zagorskii, A. A.. Three-dimensional conical fibrations. Mat. Zametki 21 (1977), 745–758; translation in Math. Notes 21 (1977), 420–427.Google Scholar
Zhang, Q.. Rational connectedness of log Q-Fano varieties. J. Reine Angew. Math. 590 (2006), 131–142.Google Scholar
Zhuang, Z.. Birational superrigidity is not a locally closed property. Selecta Math. (N.S.) 26 (2020), paper no 11, 20pp.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×