Equivariant Characteristic Classes of Singular Complex Algebraic Varieties

Sylvain Cappell, Laurentiu G. Maxim, Jörg Schürmann, Julius L. Shaneson

Research output: Contribution to journalArticle

Abstract

Homology Hirzebruch characteristic classes for singular varieties have been recently defined by Brasselet, Schüurmann, and Yokura as an attempt to unify previously known characteristic class theories for singular spaces (e.g., MacPherson-Chern classes, Baum-Fulton-MacPherson Todd classes, and Goresky-MacPherson $L$-classes). In this paper we define equivariant analogues of these classes for singular quasi-projective varieties acted upon by a finite group of algebraic automorphisms and show how these can be used to calculate the homology Hirzebruch classes of global quotient varieties. We also compute the new classes in the context of monodromy problems, e.g., for varieties that fiber equivariantly (in the complex topology) over a connected algebraic manifold. As another application, we discuss Atiyah-Meyer type formulae for twisted Hirzebruch classes of global orbifolds.

Original languageEnglish (US)
Pages (from-to)1722-1769
Number of pages48
JournalCommunications on Pure and Applied Mathematics
Volume65
Issue number12
DOIs
StatePublished - Dec 2012

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Characteristic Classes
Algebraic Variety
Equivariant
Topology
Fibers
Homology
Michael Francis Atiyah
Chern Classes
Projective Variety
Monodromy
Orbifold
Class
Automorphisms
Quotient
Finite Group
Fiber
Analogue
Calculate

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Equivariant Characteristic Classes of Singular Complex Algebraic Varieties. / Cappell, Sylvain; Maxim, Laurentiu G.; Schürmann, Jörg; Shaneson, Julius L.

In: Communications on Pure and Applied Mathematics, Vol. 65, No. 12, 12.2012, p. 1722-1769.

Research output: Contribution to journalArticle

Cappell, Sylvain ; Maxim, Laurentiu G. ; Schürmann, Jörg ; Shaneson, Julius L. / Equivariant Characteristic Classes of Singular Complex Algebraic Varieties. In: Communications on Pure and Applied Mathematics. 2012 ; Vol. 65, No. 12. pp. 1722-1769.
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