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Lefschetz properties and the Jacobian algebra of -dimensional hyperplane arrangements

  • Simone Marchesi

    Universitat de Barcelona, Spain; Centre de Recerca Matemàtica, Bellaterra, Spain
    ORCID

  • Elisa Palezzato

    Coconino Community College, Flagstaff, USA

  • Michele Torielli

    Northern Arizona University, Flagstaff, USA
    ORCID
Lefschetz properties and the Jacobian algebra of $3$-dimensional hyperplane arrangements cover
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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.

Cite this article

Simone Marchesi, Elisa Palezzato, Michele Torielli, Lefschetz properties and the Jacobian algebra of -dimensional hyperplane arrangements. Port. Math. (2025), published online first

DOI 10.4171/PM/2155