Factorization of the normalization of the Nash blowup of order $n$ of ${\mathcal{A}}_n$ by the minimal resolution

Abstract

We show that the normalization of the Nash blowup of order $n$ of the toric surface singularity ${\mathcal{A}}_n$ can be factorized by the minimal resolution of ${\mathcal{A}}_n$. The result is obtained using the combinatorial description of these objects.