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.