Free Resolutions of Simplicial Posets
Free Resolutions of Simplicial Posets
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DOI：
10.1006/jabr.1996.6855
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发表时间：
1997-02
影响因子：
0.9
通讯作者：
Art M. Duval
中科院分区：
文献类型：
--
作者：
Art M. Duval
Abstract A simplicial poset, a poset with a minimal element and whose every interval is a Boolean algebra, is a generalization of a simplicial complex. Stanley defined a ring A P associated with a simplicial poset P that generalizes the face-ring of a simplicial complex. If V is the set of vertices of P , then A P is a k [ V ]-module; we find the Betti polynomials of a free resolution of A P , and the local cohomology modules of A P , generalizing Hochster's corresponding results for simplicial complexes. The proofs involve splitting certain chain or cochain complexes more finely than in the simplicial complex case. Corollaries are that the depth of A P is a topological invariant, and that the depth may be computed in terms of the Cohen-Macaulayness of skeleta of P , generalizing results of Munkres and Hibi.
