A converse to the Andreotti-Grauert theorem

Details A converse to the Andreotti-Grauert theorem A converse to the Andreotti-Grauert theorem

2010-11-16

arxiv.org/abs/1011.3635v2

Mathematics

Algebraic Geometry

12 pages

Scientific paper

The goal of this paper is to show that there are strong relations between certain Monge-Amp\`ere integrals appearing in holomorphic Morse inequalities, and asymptotic cohomology estimates for tensor powers of holomorphic line bundles. Especially, we prove that these relations hold without restriction for projective surfaces, and in the special case of the volume, i.e. of asymptotic 0-cohomology, for all projective manifolds. These results can be seen as a partial converse to the Andreotti-Grauert vanishing theorem.

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