A resolution theorem for homology cycles of real algebraic varieties
type: Item
instance of: scholarly article
title: A resolution theorem for homology cycles of real algebraic varieties
zbMATH Open document ID: 0568.14014
DOI: 10.1007/BF01388525
author: Selman Akbulut
author: Henry C. King
published in: Inventiones Mathematicae
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143214
review text: The proof of the following result is given. Let V be a compact nonsingular real algebraic set. Then there exists an algebraic resolution \(\pi\) : \(\tilde V\to V\) such that \(H_ k(\tilde V;{\mathbb{Z}}_ 2)\) is generated by components of k-dimensional compact nonsingular algebraic subsets (precisely, stable algebraic subsets of \(\tilde V\) for all k. - The reason for this result not to be a direct consequence of Hironaka's resolution theorem is that not all homology cycles of V may be represented by algebraic subsets.
Mathematics Subject Classification ID: 14Pxx
Mathematics Subject Classification ID: 57R95
Mathematics Subject Classification ID: 14E15
zbMATH DE Number: 3906628
zbMATH Keywords: real algebraic set
zbMATH Keywords: algebraic resolution
zbMATH Keywords: stable algebraic subsets
reviewed by: Goo Ishikawa
MaRDI profile type: Publication
cites work: The topology of real algebraic sets with isolated singularities
cites work: Submanifolds and Homology of Nonsingular Real Algebraic Varieties
cites work: Real algebraic structures on topological spaces
cites work: Q4002664
cites work: Resolution of singularities of an algebraic variety over a field of characteristic zero. I
cites work: Q4128900
cites work: Q5522742
cites work: Quelques propriétés globales des variétés différentiables
description: scientific article; zbMATH DE number 3906628