On the log canonical threshold and numerical data of a resolution in dimension 2

TL;DR

This paper investigates properties of numerical data from resolutions of plane curve singularities, inspired by Igusa's conjecture on exponential sums, contributing to understanding singularity invariants.

Contribution

It introduces new properties of numerical data associated with resolutions of plane curve singularities, inspired by conjectures on exponential sums.

Findings

Identifies specific properties of numerical data in resolution processes.

Provides insights related to Igusa's conjecture on exponential sums.

Enhances understanding of singularity invariants in algebraic geometry.

Abstract

We show various properties of numerical data of an embedded resolution of singularities for plane curves, which are inspired by a conjecture of Igusa on exponential sums.