Resolving toric varieties with Nash blow-ups

Details Resolving toric varieties with Nash blow-ups Resolving toric varieties with Nash blow-ups

2009-10-27

arxiv.org/abs/0910.5028v1

Mathematics

Algebraic Geometry

22 pages, 6 tables, 3 figures

Scientific paper

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.

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