Lefschetz Properties and Hyperplane Arrangements

Abstract

In this article, we study the weak and strong Lefschetz properties, and the related notion of almost revlex ideal, in the non-Artinian case, proving that several results known in the Artinian case hold also in this more general setting. We then apply the obtained results to the study of the Jacobian algebra of hyperplane arrangements.

arXiv commentTo appear in the Journal of Algebra

References in corpus (5)

• Singular hypersurfaces characterizing the Lefschetz properties
• The strong Lefschetz property of the coinvariant ring of the Coxeter group of type H4
• Strong Lefschetz elements of the coinvariant rings of finite Coxeter groups
• Reduction numbers and initial ideals
• Generic initial ideals, graded Betti numbers and $k$-Lefschetz properties

Cited by in corpus (1)

• On the Falk invariant of Shi and Linial arrangements