论文标题
Artinian Gorenstein代数的Hilbert功能，具有强烈的Lefschetz属性
Hilbert Functions of Artinian Gorenstein algebras with the Strong Lefschetz Property
论文作者
论文摘要
我们证明，非阴性整数的序列$ h $是某些Artinian Gorenstein代数的Hilbert功能，并且仅当它是Si-sequence时才具有强烈的Lefschetz属性。这概括了T. harima的结果，该结果表征了Artinian Gorenstein代数的Hilbert功能，其特性较弱。我们还提供了从$ \ Mathbb {p}^n $中的积分理想获得的Artinian Gorenstein代数，使他们的某些高级HESSIAN具有不存在的决定因素。因此，我们为满足SLP的代数为家庭提供。
We prove that a sequence $h$ of non-negative integers is the Hilbert function of some Artinian Gorenstein algebra with the strong Lefschetz property if and only if it is an SI-sequence. This generalizes the result by T. Harima which characterizes the Hilbert functions of Artinian Gorenstein algebras with the weak Lefschetz property. We also provide classes of Artinian Gorenstein algebras obtained from the ideal of points in $\mathbb{P}^n$ such that some of their higher Hessians have non-vanishing determinants. Consequently, we provide families of such algebras satisfying the SLP.
