3 research outputs found
Equivariant characteristic classes of singular complex algebraic varieties
Homology Hirzebruch characteristic classes for singular varieties have been
recently defined by Brasselet-Schuermann-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, respectively). In this note 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.Comment: v2: updates include a motivic approach, as well as an Atiyah-Meyer
formula for global orbifolds, including a defect formul