On the canonical ideal of the Ehrhart ring of the chain polytope of a poset
On the canonical ideal of the Ehrhart ring of the chain polytope of a poset
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论偏序集链多胞形的埃尔哈特环的正则理想
DOI：
10.1016/j.jalgebra.2019.09.004
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发表时间：
2019
影响因子：
0.9
通讯作者：
Mitsuhiro Miyazaki
中科院分区：
文献类型：
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作者：
Mitsuhiro Miyazaki
设P是偏序集，O（P）是P的序多胞形，C（P）是P的链多胞形.本文研究了域K上C（P）的Ehrhart环K [C（P）]的标准理想，并刻画了其水平（分别为.特别地，我们证明了如果K [C（P）]是水平的（分别为.（1）K [O（P）]。我们展示的例子表明，匡威并不成立。证明了K [C（P）]的标准理想的符号幂与一般的符号幂相同，标准理想和反标准理想的生成元的次数是连续的整数.
Let P be a poset, O (P) the order polytope of P and C (P) the chain polytope of P. In this paper, we study the canonical ideal of the Ehrhart ring K [C (P)] of C (P) over a field K and characterize the level (resp. anticanonical level) property of K [C (P)] by a combinatorial structure of P. In particular, we show that if K [C (P)] is level (resp. anticanonical level), then so is K [O (P)]. We exhibit examples which show the converse does not hold. Moreover, we show that the symbolic powers of the canonical ideal of K [C (P)] are identical with ordinary ones and degrees of the generators of the canonical and anticanonical ideals are consecutive integers.