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Relatively minimal quasihomogeneous projective 3-folds

Published online by Cambridge University Press:  22 January 2016

Stefan Kebekus
Stefan Kebekus*
Affiliation:
Mathematisches Institut der Universität Bayreuth, 95440 Bayreuth, Germany, FAX: +49 (0)921/55-2785 stefan.kebekus@uni-bayreuth.de
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Abstract

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In the present work we classify the relatively minimal 3-dimensional quasihomogeneous complex projective varieties under the assumption that the automorphism group is not solvable. By relatively minimal we understand varieties X having at most ℚ-factorial terminal singularities and allowing an extremal contraction X → Y where dim Y < 3.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 157 , 2000 , pp. 149 - 176
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2000

References

[Băd82] Bădescu, L., On ample divisors, Nagoya Math. J., 86 (1982), 155–171.Google Scholar
[Fuj85] Fujita, T., On polarized manifolds whose adjoint bundles are not semipositive, In T. Oda, editor, Advanced Studies in Pure Mathematics, 10 (1985), North-Holland publishing company, 167–178.Google Scholar
[HO80] Huckleberry, A. and Oeljeklaus, E., Classification Theorems for Almost Homogeneous Spaces, Institut Elie Cartan, 1980.Google Scholar
[Huc90] Huckleberry, A., Actions of groups of holomorphic transformations, In Barth, Narasimhan, and Gamkrelidze, editors, Several complex variables VI. Complex manifolds, 69 (1990), Encycl. Math. Sci., Springer-Verlag, 143–196.Google Scholar
[Isk83] Iskovskih, V., Algebraic threefolds with special regard to the problem of rationality, Proc. Int. Cong. Math. at Warszawa, 1 (1984), 733–746.Google Scholar
[KMM87] Kawamata, Y., Matsuda, K. and Matsuki, K., Introduction to the minimal model problem, In T. Oda, editor, Advanced Studies in Pure Mathematics, 10 (1985), North-Holland publishing company, 283–360.Google Scholar
[Keb98] Kebekus, S., Simple models of quasihomogeneous projective 3-folds, available on the Internet at , Doc. Math. J. DMV, 3 (1998), 15–26.Google Scholar
[Keb99] Kebekus, S., On the classification of 3-dimensional SL2(C)-varieties, Nagoya Math. J., 157 (2000), ??–??.CrossRefGoogle Scholar
[Kra85] Kraft, H., Geometrische Methoden in der Invariantentheorie, Aspekte der Math-ematik, D1, Vieweg, 2, durchges. aufl. edition, 1985.Google Scholar
[LV83] Luna, D. and Vust, T., Plongements d’espaces homogènes, Comment Math. Helv., 58 (1983), 186–245.CrossRefGoogle Scholar
[Mar73] Maruyama, M., On a family of algebraic vector bundles, In Number Theory, Algebraic Geometry and Commutative Algebra, in honor of Y. Akizuki (1973), Tokyo, Kinokuniya, 95–146.Google Scholar
[MJ90] Moser-Jauslin, L., Smooth embeddings of SL(2) and PGL(2), J. Algebra, 2(132) (1990), 384–405.Google Scholar
[Mor82] Mori, S., Threefolds whose canonical bundles are not numerically effective, Ann. of Math., 116 (1982).Google Scholar
[MU83] Mukai, S. and Umemura, H., Minimal rational threefolds, In M. Raynaud and T. Shioda, editors, Algebraic geometry, Proc. Jap.-Fr. Conf., Tokyo and Kyoto 1982, Lect. Notes Math., 1016 (1983), Springer, 490–518.Google Scholar
[Mum66] Mumford, D., Lectures on curves on an algebraic surface, Princeton University Press, 1966.Google Scholar
[Rei83] Reid, M., Minimal models of canonical 3-folds, In Advanced studies in pure math., 1 (1983), Kinokuniya and North Holland, 131–180.Google Scholar
[Rei87] Reid, M., Young person’s guide to canonical singularities, Proceedings of Symposia in Pure Mathematics, 46, 1987.Google Scholar
[Win95] Winkelmann, J., The Classification of three-dimensional homogeneous complex manifolds, Lecture Notes in Mathematics, 1602, Springer, 1995.Google Scholar