论文标题
gorenstein在刺穿光谱上的gorenstein和几乎是gorenstein的特性
Gorenstein on the punctured spectrum and nearly Gorenstein property of the Ehrhart ring of the stable set polytope of an h-perfect graph
论文作者
论文摘要
在本文中，我们给出了H-Perfect图的Ehrhart环的几乎Gorenstein属性的标准：H-Perfect Graph $ g $的稳定集合的Ehrhart环，带有连接的组件$ G^{（1）}，\ ldots，g^^^$ g^^^^^^^^^^^（（iS） （1）对于每个$ i $，$ g^{（i）} $的稳定套件的ehrhart环为gorenstein和（2）$ |ω（g^{（i）}） - ω（g^{（j）}） $ g^{（i）} $。 我们还表明，Cohen-Macaulay的Segre乘积是带线性非式偏射剂的分级环，如果在穿刺频谱上是Gorenstein，则在刺穿的光谱上也是戈伦斯坦（Gorenstein），如果除了一个环是标准级别的所有环。
In this paper, we give a criterion of the nearly Gorenstein property of the Ehrhart ring of the stable set polytope of an h-perfect graph: the Ehrhart ring of the stable set polytope of an h-perfect graph $G$ with connected components $G^{(1)}, \ldots, G^{(\ell)}$ is nearly Gorenstein if and only if (1) for each $i$, the Ehrhart ring of the stable set polytope of $G^{(i)}$ is Gorenstein and (2) $|ω(G^{(i)})-ω(G^{(j)})|\leq 1$ for any $i$ and $j$, where $ω(G^{(i)})$ is the clique number of $G^{(i)}$. We also show that the Segre product of Cohen-Macaulay graded rings with linear non-zerodivisor which are Gorenstein on the punctured spectrum is also Gorenstein on the punctured spectrum if all but one rings are standard graded.
