Filling in holes of analytic surfaces and classification of compact surfaces
type: Item
instance of: scholarly article
title: Filling in holes of analytic surfaces and classification of compact surfaces
zbMATH Open document ID: 0783.32008
author: Georges Dloussky
publication date: 1994-03-13T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/75016
review text: We consider the problem of filling in holes in dimension 2 where we examine under which condition a strictly pseudoconvex hypersurface in an analytic surface is the boundary of a Stein space. We show that Rossi's example of a strictly pseudoconvex hypersurface \(\Sigma\), which bounds two nonrelatively compact domains, is not the boundary of a Stein space although holomorphic functions in a neighbourhood of \(\Sigma\) give local charts. We show that in a compact complex surface \(S\) without nonconstant meromorphic functions with \(b_ 1(S)=1\), such a phenomenon cannot exist.
Mathematics Subject Classification ID: 32E10
Mathematics Subject Classification ID: 32F10
Mathematics Subject Classification ID: 32J15
zbMATH DE Number: 490690
zbMATH Keywords: classification of surfaces
zbMATH Keywords: filling in holes
zbMATH Keywords: strictly pseudoconvex hypersurface
zbMATH Keywords: analytic surface
zbMATH Keywords: boundary of a Stein space
zbMATH Keywords: compact complex surface
MaRDI profile type: Publication
OpenAlex ID: W2087736021
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DOI: 10.5802/AIF.1352
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 490690