Non-Gorenstein loci of Ehrhart rings of chain and order polytopes
Non-Gorenstein loci of Ehrhart rings of chain and order polytopes
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链状和有序多胞体的艾哈特环的非戈伦斯坦基因座
DOI：
10.1016/j.jalgebra.2023.12.017
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发表时间：
2020
影响因子：
0.9
通讯作者：
Janet Page
中科院分区：
文献类型：
--
作者：
Mitsuhiro Miyazaki;Janet Page
设P是一个有限偏序集，K是一个域，O（P）（resp. C（P））命令（resp.我们研究了E K [O（P）]（resp. E K [C（P）]），O（P）的Ehrhart环（resp.特别地，我们证明了EK [O（P）]和EK [C（P）]的非Gorenstein轨迹的维数是相同的.进一步，我们证明了E K [C（P）]是几乎Gorenstein的当且仅当P是纯偏序集P1，…，Ps的不交并，|rank P i− rank P j|对于任何i和j，≤ 1。
Let P be a finite poset, K a field, and O (P)(resp. C (P)) the order (resp. chain) polytope of P. We study the non-Gorenstein locus of E K [O (P)](resp. E K [C (P)]), the Ehrhart ring of O (P)(resp. C (P)) over K, which are each normal toric rings associated P. In particular, we show that the dimension of non-Gorenstein loci of E K [O (P)] and E K [C (P)] are the same. Further, we show that E K [C (P)] is nearly Gorenstein if and only if P is the disjoint union of pure posets P 1,…, P s with| rank P i− rank P j|≤ 1 for any i and j.