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manuscripta mathematica

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

Characterizations of Buchsbaum complexes

  • Mitsuhiro Miyazaki
Article

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 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.

Keywords

Number Theory Algebraic Geometry Topological Group Simplicial Complex Alli 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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