Double point curves for corank \(2\) map germs from \(\mathbb{C}^2\) to \(\mathbb{C}^3\)
type: Item
instance of: scholarly article
title: Double point curves for corank \(2\) map germs from \(\mathbb{C}^2\) to \(\mathbb{C}^3\)
zbMATH Open document ID: 1245.58018
published in: Topology and its Applications
publication date: 2012-03-02T00:00:00Z
review text: This is a well-written paper which gives an instructive description of properties of finitely determined map germs \(f:(\mathbb C^{2},0) \to (\mathbb C^{3},0).\) The authors extend to corank 2 map-germs properties and formulae proved in [\textit{W. L. Marar} and \textit{D. Mond}, J. Lond. Math. Soc., II. Ser. 39, No. 3, 553--567 (1989; Zbl 0691.58015)] for corank 1 finitely determined germs. They also give an explicit description of the double point scheme in terms of elementary symmetric functions and provide explicit calculations in the corank 2 case. The final section of the paper is dedicated to the proof of the following result: the Whitney equisingularity of \(1\)-parameter families of map germs \(f_t:(\mathbb C^{2},0) \to (\mathbb C^{3},0)\) is equivalent to the constancy both of \(\mu(D(f_t))\) and \(\mu(f_t(\mathbb C^2) \cap H)\) with respect to \(t,\) where \(H \subset \mathbb C^3\) is a generic hyperplane.
reviewed by: Maria Aparecida Soares Ruas
Mathematics Subject Classification ID: 58K40
Mathematics Subject Classification ID: 32S15
Mathematics Subject Classification ID: 32S30
Mathematics Subject Classification ID: 58K65
zbMATH DE Number: 6011305
zbMATH Keywords: double point scheme
zbMATH Keywords: Whitney equisingularity
zbMATH Keywords: finitely determined map germs
zbMATH Keywords: corank 2 map-germs
author: Washington Luiz Marar
author: J. J. Nuño-Ballesteros
author: Guillermo Peñafort Sanchis
describes a project that uses: SINGULAR
MaRDI profile type: Publication
full work available at URL: j.topol.2011.09.028
OpenAlex ID: W2319883756
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DOI: 10.1016/J.TOPOL.2011.09.028
description: scientific article; zbMATH DE number 6011305