English

Nash blowup fails to resolve singularities in dimensions four and higher

Algebraic Geometry 2025-11-10 v3

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

Cite

@article{arxiv.2409.19767,
  title  = {Nash blowup fails to resolve singularities in dimensions four and higher},
  author = {Federico Castillo and Daniel Duarte and Maximiliano Leyton-Álvarez and Alvaro Liendo},
  journal= {arXiv preprint arXiv:2409.19767},
  year   = {2025}
}

Comments

To appear in Annals of Mathematics