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arXiv · 1302.5742

On the Weak Lefschetz Property for Artinian Gorenstein algebras of codimension three

Mats Boij·Juan Migliore·Rosa M. Miro'-Roig·Uwe Nagel·Fabrizio Zanello
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Abstract

We study the problem of whether an arbitrary codimension three graded artinian Gorenstein algebra has the Weak Lefschetz Property. We reduce this problem to checking whether it holds for all compressed Gorenstein algebras of odd socle degree. In the first open case, namely Hilbert function (1,3,6,6,3,1), we give a complete answer in every characteristic by translating the problem to one of studying geometric aspects of certain morphisms from $\mathbb P^2$ to $\mathbb P^3$, and Hesse configurations in $\mathbb P^2$.

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Mats Boij, Juan Migliore, Rosa M. Miro'-Roig, Uwe Nagel, Fabrizio Zanello. 2013-02-22. On the Weak Lefschetz Property for Artinian Gorenstein algebras of codimension three. https://arxiv.org/abs/1302.5742

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