Nash trivial simultaneous resolution for a family of zero-sets of Nash mappings
type: Item
instance of: scholarly article
title: Nash trivial simultaneous resolution for a family of zero-sets of Nash mappings
zbMATH Open document ID: 0955.58036
author: Satoshi Koike
published in: Mathematische Zeitschrift
publication date: 2001-03-04T00:00:00Z
review text: Let \(F(x;t)\) \((t\in J)\) be a family of Nash mappings defined over a compact Nash manifold or a family of Nash map-germs, where the parameter space \(J\) is a semialgebraic set in some Euclidean space. We prove the following finiteness theorems for the family of zero-sets \(F^{-1}(0)\): (i) There is a finite partition of \(J\) into Nash manifolds such that the family of zero-sets \(F^{-1}(0)\) admits a Nash trivial simultaneous resolution over each Nash manifold. (ii) Suppose that the dimension of the source space is at least 3. Then there is a finite partition of \(J\) into Nash manifolds such that the family of zero-sets \(F^{-1}(0)\) admits a Blow-semialgebraic trivialization along each Nash manifold.
Mathematics Subject Classification ID: 58K20
Mathematics Subject Classification ID: 58A07
Mathematics Subject Classification ID: 14P20
Mathematics Subject Classification ID: 57R45
zbMATH DE Number: 1488559
zbMATH Keywords: Nash set
zbMATH Keywords: Blow-Nash triviality
zbMATH Keywords: simultaneous resolution
zbMATH Keywords: Milnor radius
MaRDI profile type: Publication
full work available at URL: s002099900109
OpenAlex ID: W2086324125
DOI: 10.1007/S002099900109
description: scientific article; zbMATH DE number 1488559