On the uniqueness problem of bivariant Chern classes
type: Item
instance of: scholarly article
title: On the uniqueness problem of bivariant Chern classes
zbMATH Open document ID: 1074.14504
author: Shoji Yokura
published in: Documenta Mathematica
publication date: 2002-07-02T00:00:00Z
full work available at URL: https://eudml.org/doc/51737
full work available at URL: 06.html
review text: Summary: We show that the bivariant Chern class \(\gamma: {\mathbb F} \to {\mathbb H}\) for morphisms from possibly singular varieties to nonsingular varieties are uniquely determined, which therefore implies that the bivariant Chern class of \textit{J.-P. Brasselet} [Astérisque 101--102, 7--22 (1983; Zbl 0529.55009)] is unique for cellular morphisms with nonsingular target varieties. Similarly we can see that the Grothendieck transformation \(\tau : {\mathbb K}_{\text{alg}} \to {\mathbb H}_{\mathbb Q}\) constructed by \textit{W. Fulton} and \textit{R. MacPherson} [Categorical framework for the study of singular spaces, Mem. Am. Math. Soc. 243 (1981; Zbl 0467.55005)] is also unique for morphisms with nonsingular target varieties.
Mathematics Subject Classification ID: 14C17
Mathematics Subject Classification ID: 55N35
zbMATH DE Number: 1762473
zbMATH Keywords: bivariant theory
zbMATH Keywords: Chern-Schwartz-MacPherson class
zbMATH Keywords: constructible function
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1762473