Abstract
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 EK[O(P)] (resp. EK[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 EK[O(P)] and EK[C(P)] are the same. Further, we show that EK[C(P)] is nearly Gorenstein if and only if P is the disjoint union of pure posets P1, …, Ps with |rankPi−rankPj|≤1 for any i and j.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
