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 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 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 a new proof of the strong F-regularity of determinantal rings defined by minors of any size. This is joint work with Yevgeniya Tarasova.

Mathematics

Audience: advanced learners

IIT Bombay Virtual Commutative Algebra Seminar

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