Courbures et singularités réelles. (Curvatures and real singularities)
type: Item
instance of: scholarly article
title: Courbures et singularités réelles. (Curvatures and real singularities)
zbMATH Open document ID: 1022.58017
DOI: 10.1007/PL00012444
author: Nicolas Dutertre
published in: Commentarii Mathematici Helvetici
publication date: 2003-03-17T00:00:00Z
review text: Summary: Let \(f:\mathbb R^n\rightarrow\mathbb R\) be a polynomial such that \(f(0)=0\) and such that 0 is an isolated critical point of \(f\). Given \(f_t\), a one-parameter smooth deformation of \(f\), we relate the limit: \[ \lim_{\varepsilon \rightarrow 0} \lim_{t \rightarrow 0} \int_{C_t^{\varepsilon}} k dv_t, \] where \(C_t^\varepsilon=f_t^{-1}(0)\cap B_\varepsilon^n\) is the Milnor fiber and \(k\) the curvature, to topological degrees associated with \(f\) and its deformation.
Mathematics Subject Classification ID: 58K05
Mathematics Subject Classification ID: 58K60
Mathematics Subject Classification ID: 32S55
zbMATH DE Number: 1883361
zbMATH Keywords: polynomial
zbMATH Keywords: isolated critical point
zbMATH Keywords: one-parameter smooth deformation
zbMATH Keywords: Milnor fiber
zbMATH Keywords: curvature
zbMATH Keywords: topological degrees
MaRDI profile type: Publication
full work available at URL: pl00012444
OpenAlex ID: W2079691506
description: scientific article; zbMATH DE number 1883361