Nash blowups of normal toric surfaces: the case of one and two segments

TL;DR

This paper demonstrates that iterated Nash blowups can resolve singularities in certain normal toric surfaces, especially those with minimal generating sets contained within one or two segments, and extends this to examples with more segments.

Contribution

It establishes that Nash blowups resolve singularities for a class of normal toric surfaces characterized by minimal generating sets within one or two segments, and provides broader examples.

Findings

Nash blowups resolve singularities in specific toric surfaces.

Surfaces with minimal generators in one or two segments are resolved.

Examples with multiple segments also exhibit resolution.

Abstract

We show that iterating Nash blowups resolve the singularities of normal toric surfaces satisfying the following property: the minimal generating set of the corresponding semigroup is contained in one or two segments. We also provide examples with an arbitrary number of segments for which the same result holds.