Gorenstein on the punctured spectrum and nearly Gorenstein property of the Ehrhart ring of the stable set polytope of an h-perfect graph
| Autor: | Miyazaki, Mitsuhiro |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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) $|\omega(G^{(i)})-\omega(G^{(j)})|\leq 1$ for any $i$ and $j$, where $\omega(G^{(i)})$ 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. Comment: Correction of typos. arXiv admin note: text overlap with arXiv:2005.03259 |
| Databáze: | arXiv |
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