Cohen-Macaulay-ness in codimension for simplicial complexes and expansion functor

TL;DR

This paper investigates the Cohen-Macaulay properties of simplicial complexes, showing how expansion affects these properties and establishing conditions under which complexes can be derived from Buchsbaum complexes.

Contribution

It proves that the expansion of a Buchsbaum simplicial complex is Cohen-Macaulay in codimension t, and characterizes when a CM_t complex can be obtained from a Buchsbaum complex.

Findings

Expansion of Buchsbaum complexes is CM_t for optimal t

Extra assumptions on CM_t complexes allow derivation from Buchsbaum complexes

Provides conditions linking Buchsbaum and Cohen-Macaulay in codimension t

Abstract

In this paper we show that expansion of a Buchsbaum simplicial complex is $CM_t$, for an optimal integer $t\geq 1$. Also, by imposing extra assumptions on a $CM_t$ simplicial complex, we prove that it can be obtained from a Buchsbaum complex.