Nash blowup fails to resolve singularities in dimensions four and higher

Annals of Mathematics 2026

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Authors: F Gabriel Castillo, Daniel Duarte, Maximiliano Leyton-Álvarez, Alvaro Liendo
DOI: 10.4007/annals.2026.203.2.7
Cited by: 1

Abstract

In this paper we show that iterating Nash blowups or normalized Nash blowups does not resolve the singularities of algebraic varieties of dimension four or higher over an algebraically closed field of arbitrary characteristic.

Fields of Study & Subjects

Polynomial and algebraic computation Algebraic Geometry and Number Theory Advanced Differential Equations and Dynamical Systems

Publication details

Journal / source
Annals of Mathematics
Publisher
Annals of Mathematics
Volume
203
Issue
2
Publication date
1 March 2026