Equivalent condition for approximately Cohen–Macaulay complexes

2012/08/01 by Michał Lasoń
Mathematics · Psychology · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #Mathematics #Psychology #math.AC #math.CO #msc:13C14

paper · pdf · doi:10.1016/j.crma.2012.09.004

published as Comptes Rendus Mathematique 350 (2012), no. 15-16, 737-739 · final version, 3 pages

openalex publication_date 2012/08/01 · arxiv created 2014/12/11 · arxiv updated 2021/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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 J. Herzog and T. 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.

Citations

• On the full, strongly exceptional collections on toric varieties with Picard number three
• A generalization of a combinatorial theorem of macaulay
• On Sequentially Cohen-Macaulay Modules