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

Simone Marchesi; Elisa Palezzato; Michele Torielli

doi:10.4171/pm/2155

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

Simone Marchesi
, Elisa Palezzato
, Michele Torielli

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Journal	Portugaliae Mathematica
Volume	83
Issue number	1
DOIs	https://doi.org/10.4171/pm/2155
State	Published - Jan 1 2026

Keywords

Lefschetz property
freeness
hyperplane arrangements

ASJC Scopus subject areas

General Mathematics

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10.4171/pm/2155

Cite this

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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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N2 - 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.

AB - 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.

KW - Lefschetz property

KW - freeness

KW - hyperplane arrangements

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

Abstract

Keywords

ASJC Scopus subject areas

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