Non-normalized Nash blowup fails to resolve singularities in dimension three

TL;DR

This paper demonstrates that non-normalized Nash blowups are insufficient for resolving singularities in three-dimensional algebraic varieties over characteristic zero fields.

Contribution

It provides a counterexample showing that iterating non-normalized Nash blowups does not always resolve singularities in three dimensions.

Findings

Non-normalized Nash blowups can fail to resolve singularities in dimension three.

Iterating Nash blowups is not a guaranteed method for desingularization in this setting.

Abstract

In this paper we show that iterating (non-normalized) Nash blowups does not necessarily resolve the singularities of algebraic varieties of dimension three over fields of characteristic zero.