Conditions for virtually Cohen-Macaulay simplicial complexes

A simplicial complex Delta is a virtually Cohen-Macaulay simplicial complex if its associated Stanley-Reisner ring S has a virtual resolution, as defined by Berkesch, Erman, and Smith, of length codim(S). We provide a sufficient condition on Delta to be a virtually Cohen-Macaulay simplicial complex. We also introduce virtually shellable simplicial complexes, a generalization of shellable simplicial complexes. Virtually shellable complexes have the property that they are virtually Cohen- Macaulay, generalizing the well-known fact that shellable simplicial complexes are Cohen-Macaulay. (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).