English

Resolving toric varieties with Nash blow-ups

Algebraic Geometry 2009-10-28 v1 Combinatorics

Abstract

It is a long-standing question whether an arbitrary variety is desingularized by finitely many normalized Nash blow-ups. We consider this question in the case of a toric variety. We interpret the normalized Nash blow-up in polyhedral terms, show how continued fractions can be used to give an affirmative answer for a toric surface, and report on a computer investigation in which over a thousand 3- and 4-dimensional toric varieties were successfully resolved.

Keywords

Cite

@article{arxiv.0910.5028,
  title  = {Resolving toric varieties with Nash blow-ups},
  author = {Atanas Atanasov and Christopher Lopez and Alexander Perry and Nicholas Proudfoot and Michael Thaddeus},
  journal= {arXiv preprint arXiv:0910.5028},
  year   = {2009}
}

Comments

22 pages, 6 tables, 3 figures

R2 v1 2026-06-21T14:03:38.588Z