论文标题
Ehrhart环的非戈伦斯坦基因座链和阶的多面眼
Non-Gorenstein loci of Ehrhart rings of chain and order polytopes
论文作者
论文摘要
令$ p $为有限孔位，$ k $每个字段，$ o（p）$（$ $ c（p）$）订单（分别链）$ p $。我们研究了$ e_k [o（p）] $（分别$ e_k [c（p）$）的非gorenstein locus，$ o（p）$（p）$（$ c（p）$）的ehrhart环，这是每个正常折磨环相关的$ p $。特别是，我们表明$ e_k [o（p）] $和$ e_k [c（p）] $的非gorenstein loci的尺寸是相同的。此外，我们表明$ e_k [c（p）] $几乎是戈伦斯坦（Gorenstein），并且只有$ p $是纯posets $ p_1，\ ldots，p_s $ with $ | | \ m mathrm {rank} p_i------------- \ mathrm {rankrm {rank p_j} p_j} p_j | \ leq for $ i $ i $ i $ j $ $ i $。
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 $P_1, \ldots, P_s$ with $|\mathrm{rank} P_i-\mathrm{rank} P_j|\leq 1$ for any $i$ and $j$.
