Abstract
Letk be a field and Δ an abstract simplicial complex with vertex set\(V \subseteq \{ x_1 ,...,x_n \}\). In this article we study the structure of the Ext modules Ext i a (A/m (l ,k[Δ]) of the Stanley-Reisner ringk[Δ] whereA=k[x 1,...,x n ] andm l =(x 1 l ,...,x n l ). Using this structure theorem we give a characterization of Buchsbaumness ofk[Δ] by means of the length of the modules Ext i A (A/m l ,k[Δ]). That isk[Δ] is Buchsbaum if and only if for alli<dimk[Δ], the length of the modules Ext i A (A/m l ,k[Δ]) is independent ofl.
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Miyazaki, M. Characterizations of Buchsbaum complexes. Manuscripta Math 63, 245–254 (1989). https://doi.org/10.1007/BF01168875
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DOI: https://doi.org/10.1007/BF01168875