Hyperplane sections and the subtlety of the Lefschetz properties

David Cook; Uwe Nagel

doi:10.1016/j.jpaa.2011.05.007

Hyperplane sections and the subtlety of the Lefschetz properties

David Cook, Uwe Nagel

Mathematics

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	108-114
Number of pages	7
Journal	Journal of Pure and Applied Algebra
Volume	216
Issue number	1
DOIs	https://doi.org/10.1016/j.jpaa.2011.05.007
State	Published - 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: [email protected] (D. Cook II), [email protected] (U. Nagel).

Funding

✩ 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: [email protected] (D. Cook II), [email protected] (U. Nagel).

Funders	Funder number
National Security Agency	H98230-09-1-0032

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jpaa.2011.05.007

Cite this

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Hyperplane sections and the subtlety of the Lefschetz properties

Abstract

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