Equivariant characteristic classes of external and symmetric products of varieties

TL;DR

This paper develops refined generating series formulas for equivariant characteristic classes of external and symmetric products of singular complex varieties, incorporating equivariant Todd, Chern, and Hirzebruch classes with new generalizations.

Contribution

It introduces new equivariant characteristic class formulas for singular spaces, extending previous results and including twisting by symmetric group representations.

Findings

Refined generating series formulas for equivariant classes

Recovery of previous symmetric product formulas

New equivariant generalizations with representation twisting

Abstract

We obtain refined generating series formulae for equivariant characteristic classes of external and symmetric products of singular complex quasi-projective varieties. More concretely, we study equivariant versions of Todd, Chern and Hirzebruch classes for singular spaces, with values in delocalized Borel-Moore homology of external and symmetric products. As a byproduct, we recover our previous characteristic class formulae for symmetric products, and obtain new equivariant generalizations of these results, in particular also in the context of twisting by representations of the symmetric group.