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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

An algebraic version of Demailly's
asymptotic Morse inequalities


Author: Flavio Angelini
Journal: Proc. Amer. Math. Soc. 124 (1996), 3265-3269
MSC (1991): Primary 14F99; Secondary 32J99
MathSciNet review: 1389502
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Abstract | References | Similar Articles | Additional Information

Abstract: We give an elementary algebraic proof of some asymptotic estimates (called by Demailly asymptotic Morse inequalities) for the dimensions of cohomology groups of the difference of two ample line bundles on a smooth complex projective variety of any dimension.


References [Enhancements On Off] (What's this?)

  • [De1] Jean-Pierre Demailly, Champs magnétiques et inégalités de Morse pour la 𝑑”-cohomologie, Ann. Inst. Fourier (Grenoble) 35 (1985), no. 4, 189–229 (French, with English summary). MR 812325 (87d:58147)
  • [De2] Jean-Pierre Demailly, Singular Hermitian metrics on positive line bundles, Complex algebraic varieties (Bayreuth, 1990) Lecture Notes in Math., vol. 1507, Springer, Berlin, 1992, pp. 87–104. MR 1178721 (93g:32044), http://dx.doi.org/10.1007/BFb0094512
  • [De3] J.-P. Demailly, $L^{2}$ vanishing theorems for positive line bundles and adjunction theory, CIME session on Transcendental Methods in Alg. Geom.(Cetraro, Italy, July 1994), Prépublication de l'Inst. Fourier 288 (1994).
  • [Siu] Yum Tong Siu, An effective Matsusaka big theorem, Ann. Inst. Fourier (Grenoble) 43 (1993), no. 5, 1387–1405 (English, with English and French summaries). MR 1275204 (95f:32035)
  • [Tra] S. Trapani, Numerical criteria for the positivity of the difference of ample divisors, preprint (1991).

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Additional Information

Flavio Angelini
Affiliation: Département de Mathématiques, Université de Nice-Sophia-Antipolis, Parc Valrose, 06108 Nice, France
Email: angelini@math.unice.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03829-4
PII: S 0002-9939(96)03829-4
Received by editor(s): March 6, 1995
Communicated by: Eric M. Friedlander
Article copyright: © Copyright 1996 American Mathematical Society