Monodromy Zeta Function Formula for Embedded $\mathbf{Q}$-Resolutions

TL;DR

This paper generalizes A'Campo's formula to compute the monodromy zeta function for singularities using embedded $ extbf{Q}$-resolutions, which include abelian quotient singularities, with illustrative examples.

Contribution

It introduces a generalized formula for the monodromy zeta function applicable to singularities resolved via embedded $ extbf{Q}$-resolutions, expanding previous methods.

Findings

Derived a new formula for monodromy zeta functions in the $ extbf{Q}$-resolution setting

Provided examples demonstrating applications of the generalized formula

Extended the scope of monodromy computations to include quotient singularities

Abstract

In a previous work we have introduced the notion of embedded $\Q$-resolution, which essentially consists in allowing the final ambient space to contain abelian quotient singularities. Here we give a generalization of N. A'Campo's formula for the monodromy zeta function of a singularity in this setting. Some examples of its applications are shown.