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