Factorization of normalization of Nash blow-up of order n of An by the minimal resolution

TL;DR

This paper demonstrates that the normalization of the Nash blow-up of order n for the toric surface singularity An can be decomposed through its minimal resolution, utilizing combinatorial methods.

Contribution

It provides a new factorization approach linking Nash blow-up normalization to minimal resolution for An singularities using combinatorial descriptions.

Findings

Normalization of Nash blow-up factors through minimal resolution

Combinatorial methods effectively describe the factorization

Enhances understanding of singularity resolutions in toric surfaces

Abstract

We show that the normalization of the Nash blow-up of order n of the toric surface singularity An can be factorized by the minimal resolution of An. The result is obtained using the combinatorial description of these objects.