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arXiv · 2502.18149

Artinian Gorenstein algebras with binomial Macaulay dual generator

Nasrin Altafi·Rodica Dinu·Sara Faridi·Shreedevi K. Masuti·Rosa M. Miró-Roig·Alexandra Seceleanu·Nelly Villamizar
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Abstract

This paper initiates a systematic study for key properties of Artinian Gorenstein \(K\)-algebras having binomial Macaulay dual generators. In codimension 3, we demonstrate that all such algebras satisfy the strong Lefschetz property, can be constructed as a doubling of an appropriate 0-dimensional scheme in \(\mathbb{P}^2\), and we provide an explicit characterization of when they form a complete intersection. For arbitrary codimension, we establish sufficient conditions under which the weak Lefschetz property holds and show that these conditions are optimal.

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Nasrin Altafi, Rodica Dinu, Sara Faridi, Shreedevi K. Masuti, Rosa M. Miró-Roig, Alexandra Seceleanu, Nelly Villamizar. 2025-02-25. Artinian Gorenstein algebras with binomial Macaulay dual generator. https://arxiv.org/abs/2502.18149

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