Dualizing complex of the face ring of a simplicial poset

Details Dualizing complex of the face ring of a simplicial poset Dualizing complex of the face ring of a simplicial poset

2009-10-08

arxiv.org/abs/0910.1498v3

Mathematics

Commutative Algebra

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

Scientific paper

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.

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