It is a long-standing questionwhether an arbitrary variety is desingularized by finitely many normalized Nash blowups. We consider this question in the case of a toric variety. We interpret the normalized Nash blowup 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.
"Resolving Toric Varieties with Nash Blowups." Experiment. Math. 20 (3) 288 - 303, 2011.