On the canonical ideal of the Ehrhart ring of the chain polytope of a poset

Let P be a poset, O(P) the order polytope of P and b(P) the chain polytope of P. In this paper, we study the canonical ideal of the Ehrhart ring K[b(P)] of b(P) over a field K and characterize the level (resp. anticanonical level) property of K[b(P)] by a combinatorial structure of P. In particular, we show that if K[b(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[b(P)] are identical with ordinary ones and degrees of the generators of the canonical and anticanonical ideals are consecutive integers. (C) 2019 Elsevier Inc. All rights reserved.