Vertical components and flatness of Nash mappings
type: Item
instance of: scholarly article
title: Vertical components and flatness of Nash mappings
zbMATH Open document ID: 1054.32004
author: Janusz Adamus
published in: Journal of Pure and Applied Algebra
publication date: 2004-08-19T00:00:00Z
review text: Let \(f:(X,0)\to(Y,0)\) be a Nash map germ such that \((X,0)\) is a pure dimensionally reduced Nash germ and \((Y,0)\) is smooth of dimension \(n\). It is shown that the flatness of \(f\) is equivalent to the absence of algebraic vertical components, which in turn by a result of Auslander is the same as the torsion freeness of a certain \(n\)th analytic tensor product involving the local rings \({\mathcal O}_{X,0}\) and \({\mathcal O}_{Y,0}\).
Mathematics Subject Classification ID: 32C07
Mathematics Subject Classification ID: 13C11
zbMATH DE Number: 2092902
zbMATH Keywords: Nash maps
zbMATH Keywords: Nash germs
zbMATH Keywords: flatness
zbMATH Keywords: vertical components
reviewed by: Alexandru Dimca
MaRDI profile type: Publication
full work available at URL: j.jpaa.2004.02.009
OpenAlex ID: W2144347092
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DOI: 10.1016/J.JPAA.2004.02.009
description: scientific article; zbMATH DE number 2092902