Algebraic approximations in analytic geometry
type: Item
instance of: scholarly article
title: Algebraic approximations in analytic geometry
zbMATH Open document ID: 0837.32008
DOI: 10.1007/BF01884302
published in: Inventiones Mathematicae
publication date: 1995-10-19T00:00:00Z
full work available at URL: https://eudml.org/doc/144302
review text: Let \(V\) and \(W\) be affine algebraic varieties and \(K\) be a compact holomorphically convex subset of \(V\). It is proved that a holomorphic mapping \(f : K \to W\) can be uniformly approximated on \(K\) by Nash algebraic mappings \(g : K \to W\) (i.e. mappings whose components \(g_j\) satisfy polynomial equations \(P_j (z, g_j (z)) = 0)\). The result is used to prove that a reduced Stein space with isolated singularities can be exhausted by open sets that are biholomorphic to open sets in affine algebraic varieties. As a consequence it is shown that if a strongly pseudoconvex, compact CR manifold bounds a strongly pseudoconvex, compact complex manifold, then it also bounds a strongly pseudoconcave, compact complex manifold.
Mathematics Subject Classification ID: 32E10
Mathematics Subject Classification ID: 32E30
Mathematics Subject Classification ID: 32V99
Mathematics Subject Classification ID: 14M99
Mathematics Subject Classification ID: 32T99
zbMATH DE Number: 807307
zbMATH Keywords: affine algebraic variety
zbMATH Keywords: Nash algebraic functions
zbMATH Keywords: compact CR manifold
author: László Lempert
MaRDI profile type: Publication
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OpenAlex ID: W1979114245
description: scientific article; zbMATH DE number 807307