Equivariant Characteristic Classes of Singular Complex Algebraic Varieties
Article first published online: 27 SEP 2012
Copyright © 2011 Wiley Periodicals, Inc.
Communications on Pure and Applied Mathematics
Special Issue: Second Special Issue Commemorating the 75th Anniversary of the Courant Institute
Volume 65, Issue 12, pages 1722–1769, December 2012
How to Cite
Cappell, S. E., Maxim, L. G., Schürmann, J. and Shaneson, J. L. (2012), Equivariant Characteristic Classes of Singular Complex Algebraic Varieties. Comm. Pure Appl. Math., 65: 1722–1769. doi: 10.1002/cpa.21427
- Issue published online: 27 SEP 2012
- Article first published online: 27 SEP 2012
- Manuscript Received: NOV 2011
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. © 2012 Wiley Periodicals, Inc.