Linkage and F-Regularity of Determinantal Rings

Abstract In this paper, 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 in the graded setting. They showed that the generic residual intersections of a complete intersection ring with rational singularities again have rational singularities. We show that if the said complete intersection is defined by homogeneous elements and is F-rational, then in fact, its generic residual intersections are 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.