On the analyticity of smooth CR maps into a real algebraic set
type: Item
instance of: scholarly article
title: On the analyticity of smooth CR maps into a real algebraic set
zbMATH Open document ID: 1010.32019
DOI: 10.1016/S1631-073X(02)02392-0
author: Bernard Coupet
author: Sylvain Damour
author: Joël Merker
author: Alexandre Sukhov
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2002-10-14T00:00:00Z
review text: Let \(f: M \to M'\) be a \(C^\infty\)-smooth CR mapping between a generic real-analytic submanifold \(M\subset\mathbb C^n\) \((n\geqslant 2)\) and a real-algebraic subset \(M'\subset\mathbb C^{n'}\). The authors study the analyticity of such \(f\) and establish an upper bound for the transcendency degree of \(f\) as a function of the maximal dimension of local holomorphic foliation contained in \(M'\). It is proved that if \(M\) is minimal at a point \(p\) in the sense of Tumanov and if \(M'\) does not contain an open piece of complex curve, then \(f\) is real-analytic at \(p\).
Mathematics Subject Classification ID: 32V10
zbMATH DE Number: 1777397
zbMATH Keywords: CR mapping
zbMATH Keywords: generic real-analytic submanifold
zbMATH Keywords: real-algebraic subset
zbMATH Keywords: transcendency degree
zbMATH Keywords: real analytic mapping
zbMATH Keywords: local holomorphic foliation
zbMATH Keywords: meromorphic extension
zbMATH Keywords: algebraic dependence
MaRDI profile type: Publication
cites work: Q4237138
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description: scientific article; zbMATH DE number 1777397