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arXiv · 0910.5028

Resolving toric varieties with Nash blow-ups

Atanas Atanasov·Christopher Lopez·Alexander Perry·Nicholas Proudfoot·Michael Thaddeus
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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.

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Atanas Atanasov, Christopher Lopez, Alexander Perry, Nicholas Proudfoot, Michael Thaddeus. 2009-10-27. Resolving toric varieties with Nash blow-ups. https://arxiv.org/abs/0910.5028

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