On a suspension formula for Denef-Loeser zeta functions

TL;DR

This paper generalizes formulas for topological zeta functions of suspensions to the motivic level and applies stratification and toric geometry techniques to broader classes of singularities.

Contribution

It extends existing suspension formulas from topological to motivic zeta functions and introduces a stratification approach for arbitrary suspensions and complex singularities.

Findings

Derived motivic zeta function formulas for arbitrary suspensions.

Extended formulas to non-isolated singularities like superisolated and L extsuperscript{e}-Yomdin.

Utilized stratification and toric geometry techniques.

Abstract

Formulas for the topological zeta functions of suspensions by 2 points are due to Artal et al. We generalize these formulas to the motivic level and for arbitrary suspensions, by using a stratification principle and classical techniques of generating functions in toric geometry. The same strategy is used to obtain formulas for the motivic zeta functions of some families of non-isolated singularities related to superisolated, L\^e-Yomdin, and weighted L\^e-Yomdin singularities.