The weak Lefschetz property for Artinian Gorenstein algebras of codimension three

Abstract

We study the weak Lefschetz property of a class of graded Artinian Gorenstein algebras of codimension three associated in a natural way to the Apéry set of a numerical semigroup generated by four natural numbers. We show that these algebras have the weak Lefschetz property whenever the initial degree of their defining ideal is small.

arXiv commentTo appear in JPAA. 29 pages

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Cited by in corpus (3)

• On decomposing monomial algebras with the Lefschetz properties
• Enumerations of lozenge tilings, lattice paths, and perfect matchings and the weak Lefschetz property
• The weak Lefschetz property of Gorenstein algebras of codimension three associated to the Apéry sets