\(\mathcal A\)-codimension and the vanishing topology of discriminants
type: Item
instance of: scholarly article
title: \(\mathcal A\)-codimension and the vanishing topology of discriminants
zbMATH Open document ID: 0772.32023
DOI: 10.1007/BF01243911
author: James Damon
author: David Mond
published in: Inventiones Mathematicae
publication date: 1992-09-27T00:00:00Z
full work available at URL: https://eudml.org/doc/143940
review text: Let \(f:(\mathbb{C}^ n,0)\to(\mathbb{C}^ 0,0)\) be finitely \({\mathcal A}\)- determined, \(n\geq p\). If \((n,p)\) is in a range of nice dimensions in the sense of Mather then there is a deformation \(f_ t\) which has a stable representative on a neighborhood \(U\) of \(O\) called stabilization of \(f\). It is proved that the Milnor fibre of the discriminant of \(f_ t\) has the homotopy type of a wedge of \(\mu_ \Delta(f)\) spheres of dimensions \(p-1\cdot\mu_ \Delta(f)\) is called the discriminant Milnor number of \(f\). It is proved that \(\mu_ \Delta(f)=A_ e\)-codim \((f)\) and equality holds if \(f\) is weighted homogeneous (a result similar to \(\mu(f)=\tau(f)\) for singularities). If \((n,p)\) is not in a range of nice dimensions correction terms for the inequality are given.
reviewed by: Gerhard Pfister
Mathematics Subject Classification ID: 32S05
Mathematics Subject Classification ID: 32S55
zbMATH DE Number: 59800
zbMATH Keywords: \(A\)-equivalence of map germs
zbMATH Keywords: weighted homogeneous map germs
zbMATH Keywords: Milnor fibre
MaRDI profile type: Publication
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OpenAlex ID: W2327206153
description: scientific article; zbMATH DE number 59800