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

Abstract

We show that the morphism of the normalization of n-th Nash blowup of the toric surface singularity A n can be factorized by the minimal resolution of A n . It was known that the normalization of the n-th Nash blowup of a toric surface and the minimal resolution is also a toric surface. Using this, we find the essential divisor of the minimal resolution in the subdivision that defines the n-th Nash blowup. As a consequence we obtain the factorization desired.