Student Commutative Algebra Seminar

The Nash blowup of an algebraic variety replaces singular points with limits of tangent spaces associated to the variety at non-singular points. The main open problem in this topic is whether the iteration of the Nash blowup solves the singularities of the variety.
In order to be able to achieve a resolution of singularities using Nash blowups, it is needed that this process always modifies a singular variety. A classic result in this theory states that this is the case in characteristic zero. It is also known that this theorem is false in positive characteristic. In this talk, we'll introduce Nash blowups and discuss recent results by D. Duarte and L. Núñez-Betancourt showing that, with an extra hypothesis, this theorem also holds in positive characteristic.

This talk should be accessible to anyone familiar with the material covered in Math 614.
Zoom Link for the meeting: https://umich.zoom.us/j/94949291807
Speaker(s): Andrés Martínez Servellón (University of Michigan)