Nash blowup fails to resolve singularities in dimensions four and higher

• 成果类型: Article
• 署名作者: Castillo, Federico; Duarte, Daniel; Leyton-Alvarez, Maximiliano; Liendo, Alvaro
• 署名单位: Pontificia Universidad Catolica de Chile; Universidad Nacional Autonoma de Mexico; Universidad de Talca
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X; 1939-8980
• DOI: 10.4007/annals.2026.203.2.7
• 发表日期: 2026-03
• 页码: 677-694
• 关键词: Resolution of singularities; Nash blowup; toric varieties; VARIETIES

摘要

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.