Lefschetz properties of some codimension three Artinian Gorenstein algebras
Lefschetz properties of some codimension three Artinian Gorenstein algebras
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DOI：
10.1016/j.jalgebra.2023.03.005
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发表时间：
2022-03
影响因子：
0.9
通讯作者：
Nancy Abdallah;Nasrin Altafi;A. Iarrobino;A. Seceleanu;Joachim Yam'eogo
中科院分区：
文献类型：
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作者：
Nancy Abdallah;Nasrin Altafi;A. Iarrobino;A. Seceleanu;Joachim Yam'eogo
余维二 Artinian 代数具有强和弱 Lefschetz 性质，前提是特征为零或大于底阶。这些结果在多大程度上可以扩展到三个 Artinian Gorenstein 代数的余维，目前尚不清楚。尽管做了很多工作，余维三 Artinian Gorenstein 代数的强 Lefschetz 性质在很大程度上仍然是神秘的。我们的结果建立在并加强了之前的一些结果的基础上。我们在这里证明，每个标准分级余维三 Artinian Gorenstein 代数（希尔伯特函数的最大值最多为 6）都具有强 Lefschetz 性质，前提是特征为零。当特征大于A的底度时，表明A几乎是强Lefschetz，除了极值对度外，它们都是强Lefschetz。
Codimension two Artinian algebras have the strong and weak Lefschetz properties provided the characteristic is zero or greater than the socle degree. It is open to what extent such results might extend to codimension three Artinian Gorenstein algebras. Despite much work, the strong Lefschetz property for codimension three Artinian Gorenstein algebra has remained largely mysterious; our results build on and strengthen some of the previous results. We here show that every standard-graded codimension three Artinian Gorenstein algebraAhaving maximum value of the Hilbert function at most six has the strong Lefschetz property, provided that the characteristic is zero. When the characteristic is greater than the socle degree ofA, we show thatAis almost strong Lefschetz, they are strong Lefschetz except in the extremal pair of degrees.