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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: 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?)

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  • [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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Additional Information

Flavio Angelini
Affiliation: Département de Mathématiques, Université de Nice-Sophia-Antipolis, Parc Valrose, 06108 Nice, France

Received by editor(s): March 6, 1995
Communicated by: Eric M. Friedlander
Article copyright: © Copyright 1996 American Mathematical Society

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