Conditions for Virtually Cohen--Macaulay Simplicial Complexes
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915053875232768 |
|---|---|
| author | Yang, Jay Van Tuyl, Adam |
| author_facet | Yang, Jay Van Tuyl, Adam |
| contents | A simplicial complex $Δ$ 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 ${\rm codim}(S)$. We provide a sufficient condition on $Δ$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_17806 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Conditions for Virtually Cohen--Macaulay Simplicial Complexes Yang, Jay Van Tuyl, Adam Commutative Algebra Combinatorics A simplicial complex $Δ$ 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 ${\rm codim}(S)$. We provide a sufficient condition on $Δ$ 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. |
| title | Conditions for Virtually Cohen--Macaulay Simplicial Complexes |
| topic | Commutative Algebra Combinatorics |
| url | https://arxiv.org/abs/2311.17806 |