On the zero locus of ideals defining the Nash blowup of toric surfaces

TL;DR

This paper investigates the ideal that defines the Nash blowup of toric surfaces, aiming to identify an ideal whose zero locus matches the surface's singularities, thereby enhancing understanding of singularity resolution.

Contribution

It introduces a method to find specific ideals that characterize the Nash blowup and singular locus of toric surfaces, providing new insights into their geometric structure.

Findings

Identified an ideal whose blowup yields the Nash blowup of toric surfaces.

Established that the zero locus of this ideal coincides with the singular set.

Enhanced the understanding of the relationship between ideals and singularities in toric geometry.

Abstract

We consider the problem of finding an ideal whose blowup defines the Nash blowup of a toric surface and such that its zero locus coincides with the singular set of the toric surface.