On the fundamental homology classes of a real algebraic variety
type: Item
instance of: scholarly article
title: On the fundamental homology classes of a real algebraic variety
zbMATH Open document ID: 0977.14026
DOI: 10.1007/BF02674874
author: V. A. Krasnov
published in: Mathematical Notes
publication date: 2000-08-02T00:00:00Z
review text: The connected components of a non-singular real algebraic variety define mod \(2\) homology classes in the complexification. It is proven that these classes are either independent or satisfy only one relation, their sum equal to zero, provided that the mod \(2\) cohomology of the complex variety is generated by the image of the Chow ring. This includes the examples known before, such as curves, surfaces with vanishing first cohomology mod \(2\) group, complete intersections. The proof uses some properties of the cycle map.
Mathematics Subject Classification ID: 14P25
Mathematics Subject Classification ID: 14F17
Mathematics Subject Classification ID: 14C15
zbMATH DE Number: 1429629
zbMATH Keywords: real algebraic variety
zbMATH Keywords: equivariant cohomology
zbMATH Keywords: cycle map
zbMATH Keywords: Chow ring
zbMATH Keywords: vanishing
reviewed by: Eugenii I. Shustin
MaRDI profile type: Publication
cites work: Q4120687
cites work: ON HOMOLOGY CLASSES DETERMINED BY REAL POINTS OF A REAL ALGEBRAIC VARIETY
cites work: ON EQUIVARIANT GROTHENDIECK COHOMOLOGY OF A REAL ALGEBRAIC VARIETY, AND ITS APPLICATIONS
cites work: ON COHOMOLOGY CLASSES DEFINED BY THE REAL POINTS OF A REAL ALGEBRAIC GM-SURFACE
full work available at URL: https://doi.org/10.1007/bf02674874
OpenAlex ID: W2062331798
description: scientific article; zbMATH DE number 1429629