Hyperplane sections and the subtlety of the Lefschetz properties

David Cook, Uwe Nagel

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

The weak and strong Lefschetz properties are two basic properties that Artinian algebras may have. Both Lefschetz properties may vary under small perturbations or changes of the characteristic. We study these subtleties by proposing a systematic way of deforming a monomial ideal failing the weak Lefschetz property to an ideal with the same Hilbert function and the weak Lefschetz property. In particular, we lift a family of Artinian monomial ideals to finite level sets of points in projective space with the property that a general hyperplane section has the weak Lefschetz property in almost all characteristics, whereas a special hyperplane section does not have this property in any characteristic.

Original languageEnglish
Pages (from-to)108-114
Number of pages7
JournalJournal of Pure and Applied Algebra
Volume216
Issue number1
DOIs
StatePublished - Jan 2012

Bibliographical note

Funding Information:
✩ Part of the work for this paper was done while the authors were partially supported by the National Security Agency under Grant Number H98230-09-1-0032.∗ Correspondingauthor. E-mail addresses: dcook@ms.uky.edu (D. Cook II), uwe.nagel@uky.edu (U. Nagel).

ASJC Scopus subject areas

  • Algebra and Number Theory

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