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Free Resolutions of Simplicial Posets

✍ Scribed by Art M Duval

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 371 KB
Volume: 188
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1996.6855

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✦ Synopsis

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 associated with a simplicial poset P that generalizes the face-ring of a P w x simplicial complex. If V is the set of vertices of P, then A is a k V -module; we P find the Betti polynomials of a free resolution of A , and the local cohomology P modules of A , generalizing Hochster's corresponding results for simplicial com-P plexes. The proofs involve splitting certain chain or cochain complexes more finely than in the simplicial complex case. Corollaries are that the depth of A is a P 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.

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