Nagoya Mathematical Journal

Generalized Lyubeznik numbers

Luis Núñez-Betancourt and Emily E. Witt

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Given a local ring containing a field, we define and investigate a family of invariants that includes the Lyubeznik numbers but captures finer information. These generalized Lyubeznik numbers are defined in terms of D-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 generated K-algebras. These new invariants are indicators of F-singularities in characteristic p>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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Nagoya Math. J., Volume 215 (2014), 33 pages.

First available in Project Euclid: 23 July 2014

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Zentralblatt MATH identifier

Primary: 13D45: Local cohomology [See also 14B15] 13N10: Rings of differential operators and their modules [See also 16S32, 32C38]
Secondary: 13H99: None of the above, but in this section


Núñez-Betancourt, Luis; Witt, Emily E. Generalized Lyubeznik numbers. Nagoya Math. J. 215 (2014), 33 pages. doi:10.1215/00277630-2741026.

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