Lojasiewicz exponents and resolution of singularities

TL;DR

This paper presents an effective method for computing the Łojasiewicz exponent of sheaves of ideals on smooth schemes, utilizing resolution of singularities to facilitate the calculation.

Contribution

It introduces a novel algorithm that leverages resolution of singularities to compute Łojasiewicz exponents for arbitrary sheaves of ideals.

Findings

Provides an explicit algorithm for computation

Connects Łojasiewicz exponents with resolution of singularities

Enables practical calculation of exponents in algebraic geometry

Abstract

We show an effective method to compute the \L ojasiewicz exponent of an arbitrary sheaf of ideals of $\OO_X$, where $X$ is a non-singular scheme. This method is based on the algorithm of resolution of singularities.