## Nagoya Mathematical Journal

### Generalized Lyubeznik numbers

#### 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 $p\gt 0$ 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

https://projecteuclid.org/euclid.nmj/1406130497

Digital Object Identifier
doi:10.1215/00277630-2741026

Mathematical Reviews number (MathSciNet)
MR3296589

Zentralblatt MATH identifier
1318.13027

#### 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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