[Condition équivalente pour les complexes approximativement Cohen–Macaulay]
Nous donnons une condition nécessaire et suffisante pour quʼun complexe simplicial soit approximativement Cohen–Macaulay. Précisément, un complexe est approximativement Cohen–Macaulay si et seulement si lʼidéal associé à son dual dʼAlexander est engendré en deux degrés consécutifs et chacune de ses composantes a une résolution linéaire. Cela complète le résultat de J. Herzog et T. Hibi, qui démontrent quʼun complexe simplicial est séquentiellement Cohen–Macaulay si et seulement si chacune des composantes de lʼidéal associé à son dual dʼAlexander a une résolution linéaire.
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.
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@article{CRMATH_2012__350_15-16_737_0,
author = {Laso\'n, Micha{\l}},
title = {Equivalent condition for approximately {Cohen{\textendash}Macaulay} complexes},
journal = {Comptes Rendus. Math\'ematique},
pages = {737--739},
publisher = {Elsevier},
volume = {350},
number = {15-16},
year = {2012},
doi = {10.1016/j.crma.2012.09.004},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2012.09.004/}
}
TY - JOUR AU - Lasoń, Michał TI - Equivalent condition for approximately Cohen–Macaulay complexes JO - Comptes Rendus. Mathématique PY - 2012 SP - 737 EP - 739 VL - 350 IS - 15-16 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2012.09.004/ DO - 10.1016/j.crma.2012.09.004 LA - en ID - CRMATH_2012__350_15-16_737_0 ER -
%0 Journal Article %A Lasoń, Michał %T Equivalent condition for approximately Cohen–Macaulay complexes %J Comptes Rendus. Mathématique %D 2012 %P 737-739 %V 350 %N 15-16 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2012.09.004/ %R 10.1016/j.crma.2012.09.004 %G en %F CRMATH_2012__350_15-16_737_0
Lasoń, Michał. Equivalent condition for approximately Cohen–Macaulay complexes. Comptes Rendus. Mathématique, Tome 350 (2012) no. 15-16, pp. 737-739. doi : 10.1016/j.crma.2012.09.004. http://www.numdam.org/articles/10.1016/j.crma.2012.09.004/
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