We prove that the generic link of a generic determinantal ring defined by maximal minors is strongly F-regular. In the process, we strengthen a 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 positive prime characteristic. Hochster and Huneke showed that determinantal rings are strongly F-regular; however, their proof is quite involved. Our techniques allow us to give a new and simple proof of the strong F-regularity of determinantal rings defined by maximal minors.
Linkage and F-Regularity of Determinantal Rings
Yevgeniya Tarasova, University of MichiganAuthors: Vaibhav Pandey, Yevgeniya Tarasova
2023 AWM Research Symposium
Combinatorial and Homological Methods in Commutative Algebra [Organized by Francesca Gandini and Selvi Kara]