Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

An algebraic version of Demailly's asymptotic Morse inequalities

Author(s): 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: 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:

[De1]: J.-P. Demailly, Champs magnétiques et inégalités de Morse pour la d"-cohomologie, Ann. Inst. Fourier (Grenoble) 35 (1985), 189-229. MR 87d:58147
[De2]: J.-P. Demailly, Singular hermitian metrics on positive line bundles, Conf. Complex algebraic varieties (Bayreuth, April 2-6, 1990), edited by K. Hulek, T. Peternell, M. Schneider, F. Schreyer, Lecture Notes in Math., Vol. 1507, Springer-Verlag, Berlin, 1992. MR 93g:32044
[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]: Y. T. Siu, An effective Matsusaka big theorem, Ann. Inst. Fourier 43 (1993), 1387-1405. MR 95f:32035
[Tra]: S. Trapani, Numerical criteria for the positivity of the difference of ample divisors, preprint (1991).

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