Nash blowups of toric varieties in prime characteristic

2022/08/11 by Duarte, Daniel, Jeffries, Jack, Núñez-Betancourt, Luis · 4 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2208.05599

Abstract

We initiate the study of the resolution of singularities properties of Nash blowups over fields of prime characteristic. We prove that the iteration of normalized Nash blowups desingularizes normal toric surfaces. We also introduce a prime characteristic version of the logarithmic Jacobian ideal of a toric variety and prove that its blowup coincides with the Nash blowup of the variety. As a consequence, the Nash blowup of a, not necessarily normal, toric variety of arbitrary dimension in prime characteristic can be described combinatorially.

Cited by

• Classification of normal toric surfaces resolved by a single Nash blowup
• On a Computational Approach to the Nash Blowup Problem
• Logarithmic Jacobian ideals, quasi-ordinary hypersurfaces and equisingularity
• Non-normalized Nash blowup fails to resolve singularities in dimension three

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• Higher Nash blowups of normal toric varieties in prime characteristic
• Characteristic-free normalized Nash blowup of toric varieties
• On a Computational Approach to the Nash Blowup Problem
• Nash blowups in prime characteristic
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