Approximation and convergence properties of formal CR-maps
type: Item
instance of: scholarly article
title: Approximation and convergence properties of formal CR-maps
zbMATH Open document ID: 1031.32026
DOI: 10.1016/S1631-073X(02)02552-9
author: Francine Meylan
author: Nordine Mir
author: Dmitri Zaitsev
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2004-02-22T00:00:00Z
review text: Let \(M\) be a minimal real analytic CR submanifold in \(\mathbb C^n\) with \(p\in \)M, and \(M'\) a real algebraic subset in \(\mathbb C^{N'}\) with \(p'\in M'\). The authors show that any formal (holomorphic) mapping \(f: (\mathbb C^N, p) \rightarrow (\mathbb C^{N'}, p')\), sending \(M\) into \(M'\), can be approximated up to any given order at \(p\) by a convergent map sending \(M\) to \(M'\). If \(M\) is furthermore generic, any such \(g\), that is not convergent, must send (in an appropriate sense) \(M\) into the set \({\mathcal E}'\subset M'\) of points of D'Angelo infinite type. Therefore, if \(M'\) does not contain any nontrivial complex analytic subvariety through \(p'\), any formal map \(f\) sending \(M\) into \(M'\) is necessary convergent.
reviewed by: Shanyu Ji
Mathematics Subject Classification ID: 32V20
Mathematics Subject Classification ID: 32V10
zbMATH DE Number: 1874234
zbMATH Keywords: formal CR-maps
zbMATH Keywords: approximation
zbMATH Keywords: convergence
zbMATH Keywords: real analytic CR submanifold
Wikidata QID: Q58623209
MaRDI profile type: Publication
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full work available at URL: s1631-073x(02)02552-9
OpenAlex ID: W1967207311
description: scientific article; zbMATH DE number 1874234