Extension of CR mappings between generic algebraic submanifolds
type: Item
instance of: scholarly article
title: Extension of CR mappings between generic algebraic submanifolds
zbMATH Open document ID: 1098.32019
author: Slobodan M. Kojcinovic
published in: Pacific Journal of Mathematics
publication date: 2006-07-11T00:00:00Z
review text: The Author extends to the case of germs of connected algebraic generic CR submanifolds of \(\mathbb{C}^n\) of any codimension a result originally proved by \textit{M. S. Baouendi, X. Huang} and \textit{L. Rothschild} [Invent. Math. 125, No.1, 13--36 (1996; Zbl 0855.32009)] for the hypersurface case. He shows that a (germ of) CR map \(f:(M,o)\to(M',o')\), with a nonsingular Jacobian from an \(M\subset\mathbb{C}^n\) which is generic, holomorphically nondegenerate, and has a point of finite type, to an \(M'\subset\mathbb{C}^n\) of the same CR dimension and codimension holomorphically extends as a biholomorphism in a full complex neighborhood of \(o\) in \(\mathbb{C}^n\).
reviewed by: Mauro Nacinovich
Mathematics Subject Classification ID: 32V25
zbMATH DE Number: 5039936
zbMATH Keywords: CR submanifold
zbMATH Keywords: CR mapping
zbMATH Keywords: holomorphic extension
zbMATH Keywords: algebraic submanifold
MaRDI profile type: Publication
full work available at URL: pjm.2005.220.359
OpenAlex ID: W1972320628
DOI: 10.2140/PJM.2005.220.359
description: scientific article