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, Volume 63, Issue 2, pp 245–254 | Cite as

Characterizations of Buchsbaum complexes

  • Mitsuhiro Miyazaki


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 a i (A/m(l,k[Δ]) of the Stanley-Reisner ringk[Δ] whereA=k[x1,...,x n ] andm l =(x l 1 ,...,x l n ). Using this structure theorem we give a characterization of Buchsbaumness ofk[Δ] by means of the length of the modules Ext A i (A/m l ,k[Δ]). That isk[Δ] is Buchsbaum if and only if for alli<dimk[Δ], the length of the modules Ext A i (A/m l ,k[Δ]) is independent ofl.


Number Theory Algebraic Geometry Topological Group Simplicial Complex Alli 
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Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Mitsuhiro Miyazaki
    • 1
  1. 1.Department of Mathematics, Faculty of ScienceKyoto UniversityKyotoJapan

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