Dualizing complex of the face ring of a simplicial poset

Abstract

A finite poset $P$ is called "simplicial", if it has the smallest element $\hat{0}$, and every interval $[\hat{0},x]$ is a boolean algebra. The face poset of a simplicial complex is a typical example. Generalizing the Stanley-Reisner ring of a simplicial complex, Stanley assigned the graded ring $A_P$ to $P$. This ring has been studied from both combinatorial and topological perspective. In this paper, we will give a concise description of a dualizing complex of $A_P$, which has many applications.

16 pages. Simplified the proof of the main theorem. Added the remark that a theorem of Murai-Terai also holds for simplicial posets.

Cited by in corpus (1)

• Higher Cohen-Macaulay property of squarefree modules and simplicial posets