Weakly 1-complete surfaces with singularities and applications
type: Item
instance of: scholarly article
title: Weakly 1-complete surfaces with singularities and applications
zbMATH Open document ID: 1167.32009
author: Giuseppe Tomassini
author: Viorel Vâjâitu
published in: Michigan Mathematical Journal
publication date: 2009-02-20T00:00:00Z
review text: The authors show that if \(X\) is an irreducible complex surface which is weakly \(1\)-complete (i.e., for which there exists a continuous plurisubharmonic exhaustion function) and if there exists a nonconstant holomorphic function on it, then \(X\) is holomorphically convex. As an application, they show that if \(X\) is a holomorphically convex surface which is irreducible and locally irreducible, if \(A\) is a complex curve in \(X\) having no compact connected component, then \(X \backslash A\) is holomorphically convex. Several interesting remarks and examples are also presented.
reviewed by: Eugen Pascu
Mathematics Subject Classification ID: 32F17
Mathematics Subject Classification ID: 32S20
Mathematics Subject Classification ID: 32S25
Mathematics Subject Classification ID: 32E10
Mathematics Subject Classification ID: 32U10
zbMATH DE Number: 5509668
zbMATH Keywords: plurisubharmonic exhaustion function
zbMATH Keywords: cohomologically \(1\)-convex space
zbMATH Keywords: Stein space
zbMATH Keywords: holomorphically convex space
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1231770355
OpenAlex ID: W2011594550
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DOI: 10.1307/MMJ/1231770355
description: scientific article; zbMATH DE number 5509668