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

Shin-ichi Matsumura (2013)

Annales de l’institut Fourier

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. Moreover,...

Beweis einer Vermutung von Hartshorne für den Fall homogener Mannigfaltigkeiten.

Martin Lübke (1980)

Journal für die reine und angewandte Mathematik

Fibrati principali su spazi complessi $q$ -completi

Edoardo Ballico (1980)

Rendiconti del Seminario Matematico della Università di Padova

Levi-Curvature of Manifolds with a Stein Rational Fibration.

H. Azad (1985)

Manuscripta mathematica

On the embedding and compactification of $q$ -complete manifolds

Ionuţ Chiose (2006)

Annales de l’institut Fourier

We characterize intrinsically two classes of manifolds that can be properly embedded into spaces of the form $ℙ^{N} ∖ ℙ^{N - q}$ . The first theorem is a compactification theorem for pseudoconcave manifolds that can be realized as $\bar{X} ∖ (\bar{X} \cap ℙ^{N - q})$ where $\bar{X} \subset ℙ^{N}$ is a projective variety. The second theorem is an embedding theorem for holomorphically convex manifolds into $ℙ^{1} \times ℂ^{N}$ .

Twisted sheaves on complex spaces

Aldo Andreotti, Constantin Bănică (1980)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Un théorème d'algébraicité intermédiaire.

D. Barlet (1983)

Inventiones mathematicae