An equivariant version of the monodromy zeta function

TL;DR

This paper introduces an equivariant extension of the monodromy zeta function for singularities, utilizing Grothendieck rings and equivariant Lefschetz numbers, and provides a formula analogous to A'Campo's for this new invariant.

Contribution

It develops an equivariant version of the monodromy zeta function using Grothendieck rings and Lefschetz numbers, offering a new perspective on singularity invariants.

Findings

Defines an equivariant monodromy zeta function with G-set coefficients.

Provides an A'Campo type formula for the equivariant zeta function.

Connects the new invariant to classical singularity theory concepts.

Abstract

We offer an equivariant version of the classical monodromy zeta function of a singularity as a series with coefficients from the Grothendieck ring of finite G-sets tensored by the field of rational numbers. Main two ingredients of the definition are equivariant Lefschetz numbers and the lambda-structure on the Grothendieck ring of finite G-sets. We give an A'Campo type formula for the equivariant zeta function.