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

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.

💡 Research Summary

The paper surveys and extends Hodge‑theoretic analogues of the Atiyah‑Meyer signature formulae to both smooth and singular complex algebraic varieties, and uses these extensions to establish a stratified multiplicative property for genera and characteristic classes.

Starting from the classical result of Chern, Hirzebruch and Serre (σ(E)=σ(F)·σ(B) for a fiber bundle with trivial monodromy), Atiyah showed that when the monodromy is non‑trivial the signature of the total space can be expressed as σ(E)=ch^{(2)}(