Limits of tangent spaces to fibres and the \(w_ f\) condition
type: Item
instance of: scholarly article
title: Limits of tangent spaces to fibres and the \(w_ f\) condition
zbMATH Open document ID: 0798.32030
DOI: 10.1215/S0012-7094-93-07205-5
author: Adam Parusiński
published in: Duke Mathematical Journal
publication date: 1994-04-28T00:00:00Z
review text: Let \(U\) be an open neighborhood of the origin in \(\mathbb{C}^ m\) and \(f:U \to \mathbb{C}\) be a holomorphic function, \(f(0)=0\). Suppose that \(0 \in \mathbb{C}\) is the only critical value of \(f\). Let \({\mathcal L} = \{S_ i\}\) be a Whitney stratification of \(X = f^{-1}(0)\). The author proves that for each stratum \(S\) of \({\mathcal L}\) the pair \((U \backslash X,S)\) satisfies the \(w_ f\) condition in the sense of \textit{J. P. G. Henry}, \textit{M. Merle} and \textit{C. Sabbah} [Ann. Sci. Éc. Norm. Super., IV. Ser. 17, 227-268 (1984; Zbl 0551.32012)].
Mathematics Subject Classification ID: 32S60
Mathematics Subject Classification ID: 58A35
Mathematics Subject Classification ID: 57R70
zbMATH DE Number: 558996
zbMATH Keywords: Whitney condition
zbMATH Keywords: stratifications
zbMATH Keywords: \(\mu^*\)-constant strata
reviewed by: Aleksandr G. Aleksandrov
MaRDI profile type: Publication
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full work available at URL: s0012-7094-93-07205-5
OpenAlex ID: W2126251134
description: scientific article; zbMATH DE number 558996