Simplicial complexes of small codimension

Abstract

We show that a Buchsbaum simplicial complex of small codimension must have large depth. More generally, we achieve a similar result for ${\mathrm{CM}}_t$ 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 ${\mathrm{CM}}_t$ property is a topological invariant of a simplicial complex.

9 pages, 1 figure