Nagoya Mathematical Journal

Generalized Lyubeznik numbers

Luis Núñez-Betancourt and Emily E. Witt

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Abstract

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.

Article information

Source
Nagoya Math. J., Volume 215 (2014), 33 pages.

Dates
First available in Project Euclid: 23 July 2014

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1406130497

Digital Object Identifier
doi:10.1215/00277630-2741026

Mathematical Reviews number (MathSciNet)
MR3296589

Zentralblatt MATH identifier
1318.13027

Subjects
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

Citation

Núñez-Betancourt, Luis; Witt, Emily E. Generalized Lyubeznik numbers. Nagoya Math. J. 215 (2014), 33 pages. doi:10.1215/00277630-2741026. https://projecteuclid.org/euclid.nmj/1406130497


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