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arXiv · 1412.3735

Equivalent condition for approximately Cohen-Macaulay complexes

Michał Lasoń
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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.

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Michał Lasoń. 2014-12-11. Equivalent condition for approximately Cohen-Macaulay complexes. https://doi.org/10.1016/j.crma.2012.09.004

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