Nash blowup fails to resolve singularities in dimensions four and higher

From To appear in forthcoming issues by Federico Castillo, Daniel Duarte, Maximiliano Leyton-Álvarez, Alvaro Liendo

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.

Keywords
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Mathematical Subject Classification

Primary 2020: , , ,

Milestones
Received: 2024-10-04
Revised: 2025-09-24
Accepted: 3 October 2025

Authors

Federico Castillo

Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Santiago, Chile

Daniel Duarte

Centro de Ciencias Matematicas, UNAM, Morello, México

Maximiliano Leyton-Álvarez

Instituto de Matemáticas, Universidad de Talca, Talca, Chile

Alvaro Liendo

Instituto de Matemáticas, Universidad de Talca, Talca, Chile