The theory of stratification relative to a Newton polyhedron.
type: Item
instance of: scholarly article
title: The theory of stratification relative to a Newton polyhedron.
zbMATH Open document ID: 1060.58005
author: Ould M. Abderrahmane
publication date: 2004-12-20T00:00:00Z
full work available at URL: http://www.numdam.org/item
review text: A stratification of a variety \(V\) is an expression of \(V\) as the disjoint union of a locally finite sets of connected analytic manifolds, called strata, such that the boundary of each stratum is the union of a set of lower-dimensional strata. The most important notion in stratification theory is the regularity condition between strata. In this paper, the author investigates regularity conditions relative to a fixed Newton filtration in the context of stratification theory. First, the author shows a characterization of the (\(c\))-regularity condition defined by \textit{K. Bekka} [Lect. Notes Math. 1462, 42--62 (1991; Zbl 0733.58003)]. Next, the author presents a criterion for regularity conditions in terms of the defining equations of the strata and, after introducing a pseudo-metric adapted to the Newton polyhedron, obtains versions relative to the Newton filtration of the Fukui-Paunescu theorem [\textit{T. Fukui} and \textit{L. Paunescu}, Can. J. Math. 53, No. 1, 73--97 (2001; Zbl 0983.32006)]. In this approach it is possible to consider the version relative to a Newton filtration of the \((w)\)-regularity condition. It is shown that this condition implies \((c)\)-regularity condition. Finally, the author shows that the Demon-Gaffney condition [\textit{J. Damon} and \textit{T. Gaffney}, Invent. Math. 72, 335--358 (1983; Zbl 0519.58021)] implying the topological triviality of an analytic deformation of an analytic function can be expressed also in terms of Newton filtrations and proves that it implies \((c)\)-regularity condition.
reviewed by: Andrew Bucki
Mathematics Subject Classification ID: 58A35
Mathematics Subject Classification ID: 14B05
zbMATH DE Number: 2123566
zbMATH Keywords: singularities
zbMATH Keywords: stratified sets
zbMATH Keywords: Newton polyhedron
zbMATH Keywords: regularity condition
MaRDI profile type: Publication
OpenAlex ID: W2314097505
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DOI: 10.5802/AIF.2017
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 2123566