Problème de Levi et espaces holomorphiquement séparés. (The Levi problem and spaces holomorphically separable)
type: Item
instance of: scholarly article
title: Problème de Levi et espaces holomorphiquement séparés. (The Levi problem and spaces holomorphically separable)
zbMATH Open document ID: 0586.32017
DOI: 10.1007/BF01457061
published in: Mathematische Annalen
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/182922
review text: The following theorem is the main result of the paper. Let X and \(\Omega\) be analytic spaces and let \(\Pi: X\to \Omega\) be an analytic morphism with Stein fibers. If \(\Omega\) is holomorphically separable, dim X\(=n<\infty\) and the cohomology groups \(H^ p(X,{\mathcal O}_ X)\) regarded as complex vector spaces are countably dimensional (1\(\leq p\leq n-1)\) then X is a Stein space. See also the author's paper in Math. Ann. 256, 37-42 (1981; Zbl 0491.32012).
Mathematics Subject Classification ID: 32E10
Mathematics Subject Classification ID: 32C15
Mathematics Subject Classification ID: 32C35
Mathematics Subject Classification ID: 32C36
zbMATH DE Number: 3939701
zbMATH Keywords: Levi problem
zbMATH Keywords: analytic spaces
zbMATH Keywords: cohomology groups
zbMATH Keywords: Stein space
author: Bensalem Jennane
reviewed by: M. Klimek
MaRDI profile type: Publication
cites work: Q3952383
cites work: Problème de Levi et morphisme localement de Stein. (Problem of Levi and locally Stein morphism)
cites work: On sheaf cohomology and envelopes of holomorphy
cites work: Non-countable dimensions of cohomology groups of analytic sheaves and domains of holomorphy
cites work: Analytic Sheaf Cohomology Groups of Dimension n of n-Dimensional Complex Spaces
description: scientific article; zbMATH DE number 3939701