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arXiv · 2302.14797

A note on Artin Gorenstein algebras with Hilbert function (1,4,k,k,4,1)

Nancy Abdallah
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Abstract

We study the free resolutions of some Artin Gorenstein algebras of Hilbert function $(1,4,k,k,4,1)$ and we prove that all such algebras have the Strong Lefschetz property if they have the Weak Lefschetz property. In the case $k=4$ we prove that the Hilbert function alone fixes the betti table. For higher $k$ stronger conditions on the algebras are needed to fix the betti table. In particular, if the algebra is a complete intersection or if it is defined by an equigenerated ideal then the betti table is unique.

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Nancy Abdallah. 2023-02-28. A note on Artin Gorenstein algebras with Hilbert function (1,4,k,k,4,1). https://arxiv.org/abs/2302.14797

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