Simplicial complexes of small codimension

2018/06/13 by Varbaro, Matteo, Zaare-Nahandi, Rahim
#13F55 #13H10 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1806.05107

Abstract

We show that a Buchsbaum simplicial complex of small codimension must have large depth. More generally, we achieve a similar result for \rm CM_t simplicial complexes, a notion generalizing Buchsbaum-ness, and we prove more precise results in the codimension 2 case. Along the paper, we show that the \rm CM_t property is a topological invariant of a simplicial complex.

Related

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• On Codimension one Embedding of Simplicial Complexes
• Lower Bounds for Buchsbaum* Complexes
• A generalization of k-Cohen-Macaulay complexes