Characteristic-free normalized Nash blowup of toric varieties

TL;DR

This paper studies the normalized Nash blowup of toric varieties, identifying conditions that make it characteristic-independent and exploring its implications for resolving singularities across different fields.

Contribution

It introduces characteristic-free conditions for normalized Nash blowups of toric varieties and extends understanding of their resolution properties in all characteristics.

Findings

Normalized Nash blowup conditions are characteristic-independent.

Recovered known resolution results in positive characteristic.

Identified new families with non-singular normalized Nash blowups.

Abstract

We introduce conditions on cones of normal toric varieties under which the polyhedron defining the normalized Nash blowup does not depend on the characteristic of the base field. As a consequence, we deduce several results on the resolution of singularities properties of normalized Nash blowups. In particular, we recover all known results of the families that can be resolved via normalized Nash blowups in positive characteristic. We also provide new families of toric varieties whose normalized Nash blowup is non-singular in arbitrary characteristic.