Dualizing complex of the face ring of a simplicial poset

TL;DR

This paper describes the dualizing complex of the face ring associated with a simplicial poset, extending combinatorial and topological understanding of Stanley-Reisner rings.

Contribution

It provides a concise description of the dualizing complex for the face ring of a simplicial poset, a generalization of Stanley-Reisner rings.

Findings

Explicit dualizing complex description obtained

Applications in combinatorial and topological contexts demonstrated

Enhances understanding of face rings of simplicial posets

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.