A converse to the Andreotti-Grauert theorem

Jean-Pierre Demailly

Displaying similar documents to “A converse to the Andreotti-Grauert theorem”

Asymptotic cohomology vanishing and a converse to the Andreotti-Grauert theorem on surfaces

Shin-ichi Matsumura (2013)

Annales de l’institut Fourier

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In this paper, we study relations between positivity of the curvature and the asymptotic behavior of the higher cohomology group for tensor powers of a holomorphic line bundle. The Andreotti-Grauert vanishing theorem asserts that partial positivity of the curvature implies asymptotic vanishing of certain higher cohomology groups. We investigate the converse implication of this theorem under various situations. For example, we consider the case where a line bundle is semi-ample or big....

Asymptotic Morse inequalities for pseudoconcave manifolds

George Marinescu (1996)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Kähler manifolds with numerically effective Ricci class

Jean-Pierre Demailly, Thomas Peternell, Michael Schneider (1993)

Compositio Mathematica

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An effective Matsusaka big theorem

Yum-Tong Siu (1993)

Annales de l'institut Fourier

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Asymptotic Morse inequalities for analytic sheaf cohomology

Yum-Tong Siu (1985-1986)

Séminaire Bourbaki

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Nonclassical descriptions of analytic cohomology

Bailey, Toby N., Eastwood, Michael G., Gindikin, Simon G.

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Summary: There are two classical languages for analytic cohomology: Dolbeault and Čech. In some applications, however (for example, in describing the Penrose transform and certain representations), it is convenient to use some nontraditional languages. In [, and , J. Geom. Phys. 17, 231-244 (1995; Zbl 0861.22009)] was developed a language that allows one to render analytic cohomology in a purely holomorphic fashion.In this article we indicate a more general construction, which includes...