Compact subsets of holomorphy of a complex space
type: Item
instance of: scholarly article
title: Compact subsets of holomorphy of a complex space
zbMATH Open document ID: 0627.32005
author: Dau The Cap
published in: Acta Mathematica Vietnamica
publication date: 1986-01-01T00:00:00Z
review text: The purpose of this paper is to show that certain semi-global cohomology conditions (namely \(H^ p(K,{\mathcal O})=0\) for every \(p\geq 1)\) characterize those compact subsets K of holomorphy of a complex space X satisfying \(K=S{\mathcal O}(K)\), where S\({\mathcal O}(K)\) denotes the spectrum of the holomorphic function algebra. For X a Stein manifold semi-global cohomology conditions were found by \textit{R. Harvey} and \textit{R. O. Wells} jun. [Trans. Am. Math. Soc. 136, 509-516 (1969; Zbl 0175.372)]. Examples show that, in general, such compact subsets of holomorphy in a complex space can have singularities and thus other methods are used here in the proof.
Mathematics Subject Classification ID: 32E05
Mathematics Subject Classification ID: 32A38
Mathematics Subject Classification ID: 32E10
zbMATH DE Number: 4019436
zbMATH Keywords: cohomology conditions
zbMATH Keywords: spectrum
zbMATH Keywords: holomorphic function algebra
zbMATH Keywords: compact subsets of holomorphy in a complex space
reviewed by: Bruce Gilligan
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4019436