Extensions of regular mappings and the Łojasiewicz exponent at infinity
type: Item
instance of: scholarly article
title: Extensions of regular mappings and the Łojasiewicz exponent at infinity
zbMATH Open document ID: 1225.32034
author: Beata Osińska
published in: Bulletin des Sciences Mathématiques
publication date: 2011-03-17T00:00:00Z
review text: Let \(F:V\to {\mathbb C}^m\) be a regular mapping, where \(V\subset {\mathbb C}^n\) is an algebraic set of positive dimension and \(m\geq n\geq 2\), and let \({\mathcal L}_\infty(F)\) be the Łojasiewicz exponent at infinity of \(F\). The main result of the paper is the existence of a polynomial extension \(G:{\mathbb C}^n\to {\mathbb C}^m\) of \(F\) with \({\mathcal L}_\infty (G)={\mathcal L}_\infty(F)\). Moreover, some estimates of the degree of \(G\) are given.
Mathematics Subject Classification ID: 32S70
Mathematics Subject Classification ID: 14R99
zbMATH DE Number: 5867243
zbMATH Keywords: polynomial mapping
zbMATH Keywords: regular mapping
zbMATH Keywords: extension
zbMATH Keywords: Łojasiewicz exponent at infinity
MaRDI profile type: Publication
full work available at URL: j.bulsci.2010.11.002
OpenAlex ID: W2055369864
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DOI: 10.1016/J.BULSCI.2010.11.002
description: scientific article; zbMATH DE number 5867243