F-singularities of Determinantal Rings

Abstract

This chapter treats ring theoretic properties derived from the Frobenius functor in positive characteristics, related to tight closure theory. We develop them far enough to prove that determinantal rings are strongly F-regular. For deformation arguments one needs F-rationality. It is closely related to the rationality of singularities in characteristic 0, so that we can at least briefly discuss this property for determinantal rings. F-rationality is a very handy tool for the exploitation of toric and equivariant deformations. © 2022, Springer Nature Switzerland AG.