Alexander duality in Stanley-Reisner rings. (English) Zbl 1128.13014
Hibi, Takayuki (ed.), Affine algebraic geometry. Dedicated to Masayoshi Miyanishi on the occasion of his retirement from Osaka University. Osaka: Osaka University Press (ISBN 978-4-87259-226-9/hbk). 449-462 (2007).
Author’s abstract: First we survey correspondences of invariants and properties between a Stanley-Reisner ideal and its Alexander dual ideal. Next, we generalize a result by Herzog and Hibi which gives the correspondence between sequential Cohen-Macaulayness of an original complex and componentwise linear property of its Alexander dual. As an application we show that a Stanley-Reisner ring with enough large multiplicity is sequentially Cohen-Macaulay.
For the entire collection see [Zbl 1117.14002].
For the entire collection see [Zbl 1117.14002].
Reviewer: Anargyros Katsabekis (Nicosia)
MSC:
| 13F55 | Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes |
| 13D02 | Syzygies, resolutions, complexes and commutative rings |
