Nash blowups of 2-generic determinantal varieties in positive characteristic

TL;DR

This paper proves that Nash blowups of 2-generic determinantal varieties over fields of positive characteristic are non-singular by analyzing their toric structure and characteristic-free combinatorics, extending known results from characteristic zero.

Contribution

It establishes the non-singularity of Nash blowups for these varieties in positive characteristic, providing explicit toric descriptions and characteristic-independent combinatorial arguments.

Findings

Nash blowups are non-singular in positive characteristic

Explicit toric structure of 2-generic determinantal varieties

Characteristic-free combinatorial analysis

Abstract

We show that the Nash blowup of 2-generic determinantal varieties over fields of positive characteristic is non-singular. We prove this in two steps. Firstly, we explicitly describe the toric structure of such varieties. Secondly, we show that in this case the combinatorics of Nash blowups are free of characteristic. The result then follows from the analogous result in characteristic zero proved by W. Ebeling and S. M. Gusein-Zade.