Equivalent condition for approximately Cohen-Macaulay complexes
Commutative Algebra
2021-04-06 v1 Combinatorics
Abstract
We give a necessary and sufficient condition for a simplicial complex to be approximately Cohen-Macaulay. Namely it is approximately Cohen-Macaulay if and only if the ideal associated to its Alexander dual is componentwise linear and generated in two consecutive degrees. This completes the result of Herzog and Hibi who proved that a simplicial complex is sequentially Cohen-Macaulay if and only if the ideal associated to its Alexander dual is componentwise linear.
Keywords
Cite
@article{arxiv.1412.3735,
title = {Equivalent condition for approximately Cohen-Macaulay complexes},
author = {Michał Lasoń},
journal= {arXiv preprint arXiv:1412.3735},
year = {2021}
}
Comments
final version, 3 pages