The Castelnuovo-Mumford Regularity of Matrix Schubert Varieties

Abstract: The Castelnuovo-Mumford regularity of a graded module provides a measure of how complicated its minimal free resolution is. In work with Rajchogt, Ren, Robichaux, and St. Dizier, we noted that the CM-regularity of matrix Schubert varieties can be easily obtained by knowing the degree of the corresponding Grothendieck polynomial. Furthermore, we gave explicit, combinatorial formulas for these degrees for symmetric Grothendieck polynomials. In this talk, I will present a general degree formula for Grothendieck polynomials. This is joint work with Oliver Pechenik and David Speyer.

combinatorics

Audience: researchers in the topic

York University Applied Algebra Seminar