Lifting of algebraic cycles and associated homomorphisms in intersection homology.
type: Item
instance of: scholarly article
title: Lifting of algebraic cycles and associated homomorphisms in intersection homology.
zbMATH Open document ID: 0827.14012
DOI: 10.2307/2118630
published in: Annals of Mathematics. Second Series
publication date: 1995-12-11T00:00:00Z
review text: The theory of intersection homology introduced by Goresky and MacPherson has had a profound influence on many areas of mathematics in the last decade and a half. Intersection homology has many advantages over other sorts of homology, but suffers from the disadvantage that it is not functorial in a natural sense. This paper provides an important partial remedy to this. The authors show that if \(f : X \to Y\) is a morphism of complex algebraic varieties of pure dimension, then there exist (not necessarily unique) homomorphisms \(\nu_f : IH_* (X) \to IH_* (Y)\) of intersection homology with rational coefficients and compact support for the middle perversity, called by the authors ``associated homomorphisms'', such that the comparison homomorphisms \(IH_* (X) \to H_* (X)\) and \(IH_* (Y) \to H_* (Y)\) fit into a commutative square with \(\nu_f\) and \(f_* : H_* (X) \to H_* (Y)\). The authors deduce that homology classes of algebraic cycles admit liftings in intersection homology with rational coefficients having support arbitrarily close to the given cycles.
reviewed by: Frances Kirwan
Mathematics Subject Classification ID: 14F43
Mathematics Subject Classification ID: 14C25
Mathematics Subject Classification ID: 32S60
zbMATH DE Number: 750766
zbMATH Keywords: intersection homology
zbMATH Keywords: algebraic cycles
zbMATH Keywords: liftings
author: Gottfried Barthel
author: Jean-Paul Brasselet
author: Karl-Heinz Fieseler
author: Ofer Gabber
author: Ludger Kaup
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2307/2118630
OpenAlex ID: W2059329973
Wikidata QID: Q102442719
description: scientific article; zbMATH DE number 750766