Alexander duality for Stanley-Reisner rings and squarefree \(\mathbb{N}^n\)-graded modules
This paper introduces the notion of squarefree modules which generalizes Stanley-Reisner rings and which includes their syzygies and Ext modules. For a squarefree module the author constructs a chain complex of free modules, which is acyclic if the given module is Cohen-Macaulay. This complex is very convenient for the study of the Alexander duality. As a consequence, the author obtains results on the minimal resolutions of Stanley-Reisner rings which recover recent results of Herzog and others on componentwise linear ideals. The readers are advised to look also at recent related works on Alexander duality by \textit{E. Miller} [J. Algebra 231, 180-234 (2000; Zbl 0968.13009)] and \textit{T. Römer} [Osaka J. Math. 38, 469-485 (2001; see the following review Zbl 0981.13012].
minimal resolutions of Stanley-Reisner rings
scientific article; zbMATH DE number 1429461