Hostname: page-component-848d4c4894-hfldf Total loading time: 0 Render date: 2024-05-18T12:30:36.163Z Has data issue: false hasContentIssue false
  • English
  • Français

Algebraic Barth-Lefschetz theorems

Published online by Cambridge University Press:  22 January 2016

Lucian Bădescu
Lucian Bădescu*
Affiliation:
Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, Ro- 70700, Bucharest, Romania and University of Bucharest, Department of Mathematics, E-mail address: lbadescu@stoilow.imar.ro
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We shall work over a fixed algebraically closed field k of arbitrary characteristic. By an algebraic variety over k we shall mean a reduced algebraic scheme over k. Fix a positive integer n and e = (e0, el,…, en) a system of n + 1 weights (i.e. n + 1 positive integers e0, el,…, en). If k[T0, Tl,…, Tn] is the polynomial k-algebra in n + 1 variables, graded by the conditions deg(Ti) = ei i = 0, 1,…, n, denote by Pn(e) = Proj(k[T0, T1,…, Tn]) the n-dimensional weighted projective space over k of weights e. We refer the reader to [3] for the basic properties of weighted projective spaces.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 142 , June 1996 , pp. 17 - 38
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1996

References

[ 1 ] Bädescu, L. and Ballico, E., Formal rational functions along zero loci of sections of ample vector bundles, Rev. Roumaine Math. Pures Appl., 38 (1993), 609–630.Google Scholar
[ 2 ] Deligne, P., Le groupe fondamental du complément d’une courbe plane n’ayant que des points doubles ordinaires, Séminaire Bourbaki No 543, Paris, Novembre 1979.Google Scholar
[ 3 ] Dolgachev, I., Weighted projective varieties, Lecture Notes in Math., vol. 956, Springer Verlag, Berlin-Heidelberg-New York, 1982, pp. 34–71.Google Scholar
[ 4 ] Faltings, G., A contribution to the theory of formal meromorphic functions, Nagoya Math. J., 77 (1980), 99–106.Google Scholar
[ 5 ] Fulton, W. and Hansen, J., A connectedness theorem for projective varieties with applications to intersections and singularities of mappings, Annals of Math., 110 (1979), 159–166.Google Scholar
[ 6 ] Fulton, W. and Lazarsfeld, R., Connectivity and its applications in algebraic geometry, Lecture Notes in Math., vol. 862, Springer Verlag, Berlin-Heidelberg-New York, 1981, pp. 26–92.Google Scholar
[ 7 ] Gieseker, D., Flat bundles and the fundamental group in non-zero characteristics, Annali Sc. Norm. Pisa, 2 (1975), 1–31.Google Scholar
[ 8 ] Grothendieck, A., Revêtements étales et groupe fondamental, Lecture Notes in Math., vol. 224, Springer Verlag, Berlin-Heidelberg-New York, 1971.Google Scholar
[ 9 ] Grothendieck, A., Cohomologie locale des faisceaux cohérents et théorèmes de Lefschetz locaux et globaux, North Holland, Amsterdam, 1968.Google Scholar
[10] Grothendieck, A., Dix éxposés sur la cohomologie des schémas, North Holland, Amsterdam, 1968.Google Scholar
[11] Grothendieck, A., Local cohomology, Lecture Notes in Math. vol. 41, Springer Verlag, Berlin-Heidelberg-New York, 1966.Google Scholar
[12] Hansen, J., Higher order singularities and morphisms to projective spaces, Proc. Amer. Math. Soc, 97 (1986), 226–232.Google Scholar
[13] Hartshorne, R., Complete intersections and connectedness, Amer. J. Math., 84 (1962), 497–508.Google Scholar
[14] Hartshorne, R., Algebraic Geometry, Springer Verlag, Berlin-Heidelberg-New York, 1977.Google Scholar
[15] Hartshorne, R., Ample subvarieties of algebraic varieties, Lecture Notes in Math., vol. 156, Springer Verlag, Berlin-Heidelberg-New York, 1970.Google Scholar
[16] Hironaka, H. and Matsumura, H., Formal functions and formal embeddings, J. Math. Soc. Japan, 20 (1968), 52–82.Google Scholar
[17] Kleiman, S., On the vanishing of Hn(X, F) for an w-dimensional variety, Proc. Amer. Math. Soc, 18 (1967), 940–944.Google Scholar
[18] Ogus, A., Local cohomological dimension of algebraic varieties, Annals of Math., 98 (1973), 327–365.Google Scholar
[19] Serre, J.-P., Algebre locale, Multiplicités, Lecture Notes in Math., vol. 11, Springer Verlag, Berlin-Heidelberg-New York, 1965.Google Scholar
[20] Speiser, R., Cohomological dimension of abelian varieties, Amer. J. Math., 95 (1973), 1–34.Google Scholar
[21] Speiser, R., Projective varieties of low codimension in characteristic p > 0, Trans. Amer. Math. Soc, 240 (1978), 329–343.Google Scholar
[22] Zariski, 0., Theory and applications of holomorphic functions on algebraic varieties over arbitrary ground fields, Memoirs of the American Math. Soc, vol. 5, Rhode Island, 1951.Google Scholar