循环图稳定集多面体Ehrhart环的非Gorenstein轨迹和几乎Gorenstein性质

Pub Date : 2022-05-03 DOI:10.11650/tjm/221104

Mitsuhiro Miyazaki

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引用次数: 2

摘要

设$R$是非Gorenstein的循环图的稳定集多面体的Ehrhart环。我们描述了$\mathrm{Spec}R$的非Gorenstein轨迹。此外，我们证明了$R$几乎是Gorenstein。此外，我们还证明了Hibi和Tsuchiya的猜想是正确的。

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Non-Gorenstein Locus and Almost Gorenstein Property of the Ehrhart Ring of the Stable Set Polytope of a Cycle Graph

Let $R$ be the Ehrhart ring of the stable set polytope of a cycle graph which is not Gorenstein. We describe the non-Gorenstein locus of $\mathrm{Spec} R$. Further, we show that $R$ is almost Gorenstein. Moreover, we show that the conjecture of Hibi and Tsuchiya is true.

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