Virtual Commutative Algebra Seminar
Friday, 3 March 2023, 6:30pm
==============================
Venue: meet.google.com/mjq-ahwy-oxo
Speaker: Vaibhav Pandey
Affiliation: Purdue University, West Lafayette, IN, USA
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 strongly F-regular, hence it has rational singularities. In the process, we strengthen the result of Chardin and Ulrich. They showed that the generic residual intersections of a complete intersection ring with rational singularities again have rational singularities. We show that they are, in fact, strongly F-regular.
In the mid-1990s, Hochster and Huneke showed that generic determinantal rings are strongly F-regular; however, their proof is quite involved. The techniques that we discuss will allow us to give a new and simple proof of the strong F-regularity of generic determinantal rings defined by maximal minors. Time permitting, we will also share new proof of the strong F-regularity of determinantal rings defined by minors of any size. This is joint work with Yevgeniya Tarasova.