Commutative Algebra Seminar

Title

Linkage and F-regularity of generic determinantal rings

Abstract

We prove that the generic link of a generic determinantal ring of maximal minors is F-regular. In the process, we strengthen a result of Chardin and Ulrich. Their result says that the generic residual intersections of a complete intersection ring with rational singularities again has rational singularities. We prove that they are, in fact, F-regular.

In the mid 90s, Hochster and Huneke proved that generic determinantal rings are F-regular; however, their proof is quite involved. We give a new and simple proof of the F-regularity of determinantal rings of maximal minors. Time permitting, we will also give a new proof of the F-regularity of generic determinantal rings of minors of any size. This is joint work with Yevgeniya Tarasova.