On Serre duality
type: Item
instance of: scholarly article
title: On Serre duality
zbMATH Open document ID: 0951.32006
DOI: 10.1016/S0007-4497(00)00126-3
author: Christine Laurent-Thiébaut
author: Jürgen Leiterer
published in: Bulletin des Sciences Mathématiques
publication date: 2000-12-13T00:00:00Z
review text: The authors prove a separation criterion for the compactly supported Dolbeault cohomology. As an application they obtain a new simple proof of an Andreotti-Vesentini separation theorem which was first obtained by G.~Henkin and J.~Leiterer by means of a rather difficult proof: Let \(X\) be an \(n\)-dimensional complex manifold which is \((n-q)\)-convex in the sense of Andreotti-Grauert, \(1\leqslant q\leqslant n-1.\) Let \(K\) be a compact subset of \(X\) which admits a basis of strictly \(q\)-convex neighborhoods. Then \(H^{p,n-q}(X\setminus K,E)\) is separated for all \(p\) and each holomorphic vector bundle \(E\) over \(X.\) Note that this result is stronger than the corresponding result of Henkin-Leiterer. It is proved that the classical Andreotti-Vesentini separation theorem for \(q\)-concave manifolds holds also for any increasing union of such manifolds.
Mathematics Subject Classification ID: 32C37
Mathematics Subject Classification ID: 32L05
Mathematics Subject Classification ID: 32F10
zbMATH DE Number: 1436204
zbMATH Keywords: Serre duality
zbMATH Keywords: separation criterion for the compactly supported Dolbeault cohomology
zbMATH Keywords: Andreotti-Vesentini separation theorem
zbMATH Keywords: holomorphic vector bundle
zbMATH Keywords: Fréchet spaces
zbMATH Keywords: Andreotti-Grauert theory
MaRDI profile type: Publication
full work available at URL: s0007-4497(00)00126-3
OpenAlex ID: W1967020543
description: scientific article; zbMATH DE number 1436204