Abstract
AbstractGiven a local ring containing a field, we define and investigate a family of invariants that includes the Lyubeznik numbers but captures finer information. Thesegeneralized Lyubeznik numbersare defined in terms ofD-modules and are proved well defined using a generalization of the classical version of Kashiwara’s equivalence for smooth varieties; we also give a definition for finitely generatedK-algebras. These new invariants are indicators ofF-singularities in characteristicp >0 and have close connections with characteristic cycle multiplicities in characteristic zero. We characterize the generalized Lyubeznik numbers associated to monomial ideals and compute examples of those associated to determinantal ideals.
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