On the Lipschitz saturation of toric singularities

TL;DR

This paper explores Lipschitz saturation in toric singularities, proving that for certain cases it preserves the toric structure and providing methods to compute saturation from defining semigroups.

Contribution

It introduces the concept of Lipschitz saturation for toric singularities and demonstrates its preservation under specific conditions, along with computational techniques.

Findings

Lipschitz saturation of toric singularities with smooth normalization remains toric.

Methods to compute Lipschitz saturation from semigroups are developed.

Examples of saturation calculations for specific families are provided.

Abstract

We begin the study of Lipschitz saturation for germs of toric singularities. By looking at their associated analytic algebras, we prove that if (X,0) is a germ of toric singularity with smooth normalization then its Lipschitz saturation is again toric. Finally we show how to calculate the Lipschitz saturation for some families of toric singularities starting from the semigroup that defines them.