Ilya Smirnov: Singularities of square-free supported polynomials

Abstract: 

This talk is based on arXiv: 2501.16198, joint with Conca, De Stefani, and Núñez-Betancourt.

We say that a polynomial f is square-free supported if every monomial of f is square-free. The purpose of the talk is to explain why the hypersurface singularity defined by an irreducible polynomial with square-free support is F-rational over a field of positive characteristic. This recovers and generalizes the work of Bath-Mustata-Walther, who showed that such polynomials have only rational singularities over a field of characteristic 0.