Determination of the real poles of the Igusa zeta function for curves

TL;DR

This paper characterizes which real candidate poles are actual poles of Igusa's p-adic zeta function specifically for algebraic curves, based on numerical data from embedded resolutions.

Contribution

It provides a complete general criterion for identifying real poles of Igusa's zeta function in the case of curves, advancing understanding of their pole structure.

Findings

Identifies all real candidate poles that are actual poles for curves.

Uses numerical data from embedded resolutions to determine poles.

Provides a complete characterization in the curve case.

Abstract

The numerical data of an embedded resolution determine the candidate poles of Igusa's p-adic zeta function. We determine in complete generality which real candidate poles are actual poles in the curve case.