On the Weak Lefschetz Property for artinian Gorenstein algebras of codimension three

Mats Boij, Juan Migliore, Rosa M. Miró-Roig, Uwe Nagel, Fabrizio Zanello

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

We study the problem of whether an arbitrary codimension three graded artinian Gorenstein algebra has the Weak Lefschetz Property. We reduce this problem to checking whether it holds for all compressed Gorenstein algebras of odd socle degree. In the first open case, namely Hilbert function (1, 3, 6, 6, 3, 1), we give a complete answer in every characteristic by translating the problem to one of studying geometric aspects of certain morphisms from P2 to P3, and Hesse configurations in P2.

Original languageEnglish
Pages (from-to)48-68
Number of pages21
JournalJournal of Algebra
Volume403
DOIs
StatePublished - Feb 1 2014

Keywords

  • Artinian algebra
  • Gorenstein algebra
  • Hesse configuration
  • Primary
  • Secondary
  • Weak Lefschetz Property

ASJC Scopus subject areas

  • Algebra and Number Theory

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