An algebraic version of Demailly’s asymptotic Morse inequalities

Angelini, Flavio

doi:10.1090/S0002-9939-96-03829-4

An algebraic version of Demailly’s asymptotic Morse inequalities
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by Flavio Angelini PDF

Proc. Amer. Math. Soc. 124 (1996), 3265-3269 Request permission

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

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, DOI 10.5802/aif.1034
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, DOI 10.1007/BFb0094512
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).
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, DOI 10.5802/aif.1378
S. Trapani, Numerical criteria for the positivity of the difference of ample divisors, preprint (1991).