Sur la convergence d'applications formelles entre sous-variétés analytiques réelles. (On the convergence of formal mappings between real-analytic submanifolds)
type: Item
instance of: scholarly article
title: Sur la convergence d'applications formelles entre sous-variétés analytiques réelles. (On the convergence of formal mappings between real-analytic submanifolds)
zbMATH Open document ID: 1019.32023
DOI: 10.1016/S0007-4497(02)01144-2
author: Sylvain Damour
author: Joël Merker
published in: Bulletin des Sciences Mathématiques
publication date: 2003-03-23T00:00:00Z
review text: Let \(M\subset\mathbb{C}^n \simeq\mathbb{R}^{2n}\) be a real analytic submanifold of codimension \(d\geq 1\) defined in a neighborhood of \(o\) and let \(M' \subset \mathbb{C}^{n'}\) be a real analytic set in \(\mathbb{C}^{n'}\) with \(o\in M\), \(o\in M'\) and let \(f\) be a formal map between \(M\) and \(M'\) with \(f(o)=o\). The authors give new sufficient conditions for \(f\) to be convergent. In fact, inspired by a number of previous results by H. Lewy and others, the authors introduce the notion of first characteristic variety associated to \((M, M',f)\), and prove that if \(M\) is minimal at \(o\) and the first characteristic variety \({\mathcal V}_1\) is of dimension \(0\) at \(o\) then \(f\) is convergent. In the case when \({\mathcal V}_1\) is of positive dimension the authors introduce the notion of the second characteristic variety \({\mathcal V}_2\) and prove a similar result as above.
Mathematics Subject Classification ID: 32V25
Mathematics Subject Classification ID: 32V40
Mathematics Subject Classification ID: 32H02
Mathematics Subject Classification ID: 32H40
Mathematics Subject Classification ID: 32V10
zbMATH DE Number: 1886880
zbMATH Keywords: real-analytic manifold
zbMATH Keywords: Segre variety
zbMATH Keywords: reflection principle
zbMATH Keywords: formal mapping
reviewed by: Akihiko Morimoto
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1886880