Displaying similar documents to “Asymptotic Morse inequalities for analytic sheaf cohomology”

Holomorphic Morse Inequalities on Manifolds with Boundary

Robert Berman (2005)

Annales de l’institut Fourier

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Let X be a compact complex manifold with boundary and let L k be a high power of a hermitian holomorphic line bundle over X . When X has no boundary, Demailly’s holomorphic Morse inequalities give asymptotic bounds on the dimensions of the Dolbeault cohomology groups with values in L k , in terms of the curvature of L . We extend Demailly’s inequalities to the case when X has a boundary by adding a boundary term expressed as a certain average of the curvature of the line bundle and the Levi curvature of...

A converse to the Andreotti-Grauert theorem

Jean-Pierre Demailly (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

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The goal of this paper is to show that there are strong relations between certain Monge-Ampère 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...

Corrigendum to: Holomorphic Morse inequalities on manifolds with boundary

Robert Berman (2008)

Annales de l’institut Fourier

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A statement in the paper “Holomorphic Morse inequalities on manifolds with boundary” saying that the holomorphic Morse inequalities for an hermitian line bundle L over X are sharp as long as L extends as semi-positive bundle over a Stein-filling is corrected, by adding certain assumptions. A more general situation is also treated.