Hodge-theoretic Atiyah-Meyer formulae and the stratified multiplicative property

TL;DR

This paper surveys Hodge-theoretic Atiyah-Meyer formulae for algebraic varieties, introduces new applications, and extends classical signature formulas to singular varieties, enhancing understanding of characteristic classes.

Contribution

It provides a comprehensive survey of Atiyah-Meyer type formulae and extends signature formulas to singular varieties, offering new insights and applications.

Findings

Hodge-theoretic formulae for algebraic varieties

Extensions of signature formulas to singular settings

New applications of characteristic class formulae

Abstract

In this note we survey Hodge-theoretic formulae of Atiyah-Meyer type for genera and characteristic classes of complex algebraic varieties, and derive some new and interesting applications. We also present various extensions to the singular setting of the Chern-Hirzebruch-Serre signature formula.