Nonisomorphic algebraic models of a smooth manifold
type: Item
instance of: scholarly article
title: Nonisomorphic algebraic models of a smooth manifold
zbMATH Open document ID: 0714.14012
DOI: 10.1007/BF01459234
author: Wojciech Kucharz
author: Jacek Bochnak
published in: Mathematische Annalen
publication date: 1991-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164807
review text: The paper contains the following result. Let M be a compact \(C^{\infty}\) manifold. Then there exists an uncountable family \(\{X_{\alpha}\}_{\alpha \in \Lambda}\) of nonsingular algebraic subsets of \({\mathbb{R}}^ n\), \(n=2\cdot \dim (M)+1,\) such that each \(X_{\alpha}\) is diffeomorphic to M, and \(X_{\alpha}\) is not birationally equivalent to \(X_{\beta}\) for \(\alpha\neq \beta\).
Mathematics Subject Classification ID: 14E05
Mathematics Subject Classification ID: 57R50
zbMATH DE Number: 4175129
zbMATH Keywords: algebraic models of smooth manifolds
zbMATH Keywords: birational equivalence
MaRDI profile type: Publication
cites work: The topology of real algebraic sets with isolated singularities
cites work: Q3916680
cites work: Algebraic models of smooth manifolds
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cites work: Q3277840
description: scientific article; zbMATH DE number 4175129