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Generalized Lyubeznik numbers

Published online by Cambridge University Press:  11 January 2016

Luis Núñez-Betancourt  and
Emily E. Witt
Luis Núñez-Betancourt
Affiliation:
Department of Mathematics, University of Virginia, Charlottesville, Virginia 22904, USA, lcn8m@virginia.edu
Emily E. Witt
Affiliation:
Department of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455, USA, ewitt@umn.edu
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Abstract

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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.

Keywords

13D4513N1013H99
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 215 , September 2014 , pp. 169 - 201
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2014

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