Recognizing unstable equidimensional maps, and the number of stable projections of algebraic hypersurfaces
type: Item
instance of: scholarly article
title: Recognizing unstable equidimensional maps, and the number of stable projections of algebraic hypersurfaces
zbMATH Open document ID: 0937.58008
published in: Manuscripta Mathematica
publication date: 2000-06-13T00:00:00Z
review text: A smooth \(({\mathcal C}^\infty\) or analytic) map is unstable if it has positive \({\mathcal A}_e\)-codimension as an \(s\)-germ for some set of source points \(x_1,x_2, \dots, x_s\). The author studies the recognition of unstable maps in families \(F\) of equidimensional corank-1 maps, both in the local situation where \(F\) is an unfolding germ and in the global situation where \(F\) is the restriction of the family of all (central or parallel) projections into hyperplates to a smooth hypersurface given as the zero-set of some smooth function. Using these recognition conditions, he deduces certain local and global properties of the bifurcation set \({\mathcal B}\) in the parameter space of \(F\).
Mathematics Subject Classification ID: 58C25
Mathematics Subject Classification ID: 14J70
Mathematics Subject Classification ID: 58K20
zbMATH DE Number: 1310199
zbMATH Keywords: analytic map
zbMATH Keywords: equidimensional map
zbMATH Keywords: stable projection
author: Joachim H. Rieger
reviewed by: Vasil G. Angelov
MaRDI profile type: Publication
full work available at URL: s002290050163
OpenAlex ID: W2061915121
DOI: 10.1007/S002290050163
description: scientific article; zbMATH DE number 1310199