Computing equivariant characteristic classes of singular varieties

TL;DR

This paper develops methods to compute equivariant characteristic classes, specifically Hirzebruch classes, for singular algebraic varieties with torus actions, including localization techniques and examples.

Contribution

It extends classical theory to singular varieties with torus actions, providing explicit localization formulas and computational examples.

Findings

Localization of Hirzebruch class at fixed points

Explicit computations for specific singular varieties

Extension of classical characteristic class theory

Abstract

The paper is based on a talk. Complete exposition is given in "Equivariant Hirzebruch class for singular varieties". Starting from the classical theory we describe Hirzebruch class and the related Todd genus of a complex singular algebraic varieties. When the variety is equipped with an action of an algebraic torus we localize the Hirzebruch class at the fixed points of the action. We give some examples of computations.