Lefschetz properties and the Jacobian algebra of $3$-dimensional hyperplane arrangements

Simone Marchesi; Elisa Palezzato; Michele Torielli

doi:10.4171/pm/2155

JournalspmVol. 83, No. 1/2pp. 1–18

Lefschetz properties and the Jacobian algebra of $3$ -dimensional hyperplane arrangements

Simone Marchesi
Universitat de Barcelona, Spain; Centre de Recerca Matemàtica, Bellaterra, Spain
Elisa Palezzato
Coconino Community College, Flagstaff, USA
- MathSciNet
- zbMATH Open
Michele Torielli
Northern Arizona University, Flagstaff, USA

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Abstract

In this article, we prove that the weak and strong Lefschetz properties hold, and, moreover, are equivalent, for any quotient ring at least 2-dimensional. Furthermore, we prove that the weak Lefschetz property holds for any dimension 1 almost complete intersection. We then apply the obtained results to the case of Jacobian ideals of hyperplane arrangements.

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Simone Marchesi, Elisa Palezzato, Michele Torielli, Lefschetz properties and the Jacobian algebra of $3$ -dimensional hyperplane arrangements. Port. Math. 83 (2026), no. 1/2, pp. 1–18

DOI 10.4171/PM/2155