Strong F-regularity and generating morphisms of local cohomology modules

Abstract

We establish a criterion for the strong F-regularity of a (non-Gorenstein) Cohen–Macaulay reduced complete local ring of dimension at least 2 and prime characteristic p. We also describe an explicit generating morphism (in the sense of Lyubeznik) for the top local cohomology module with support in certain ideals arising from an n×(n−1) matrix X of indeterminates. For a perfect field k of characteristic p≥5, these results led us to derive a simple, new proof of the well-known fact that the generic determinantal ring over k given by the maximal minors of X is strongly F-regular.