Toric Nash Blowups

Hironaka's celebrated resolution of singularities in characteristic 0 proceeds via blowups of carefully chosen subvarieties. There exists an alternative canonical process (requiring no choices) called Nash blowup, and a fundamental question is whether iterated Nash blowups resolve singularities. We show that this is not the case in dimensions greater than 3, and in all characteristics, by constructing counterexamples using toric varieties. In this context the problem becomes a concrete polyhedral problem about rational cones and their Hilbert bases.
This is joint work with Daniel Duarte, Maximiliano Leyton, and Alvaro Liendo.

Bio
https://www.mat.uc.cl/~federico.castillo/