Nash blowups of 2-generic determinantal varieties in positive characteristic

2024/09/07 by Thaís M. Dalbelo, Dalbelo, Thaís M., Daniel Duarte +3 · 4 citations
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2409.04688

openalex publication_date 2024/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Classification of normal toric surfaces resolved by a single Nash blowup
• On a Computational Approach to the Nash Blowup Problem
• Non-normalized Nash blowup fails to resolve singularities in dimension three
• The Euler characteristic of Milnor fibers over 2-generic symmetric determinantal varieties

Related

• Nash blowups in prime characteristic
• Nash blowups of toric varieties in prime characteristic
• Characteristic-free normalized Nash blowup of toric varieties
• Higher Nash blowups of normal toric varieties in prime characteristic
• Higher Nash blowup on normal toric varieties