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manuscripta mathematica

, Volume 104, Issue 1, pp 39–48 | Cite as

Cohen–Macaulayness and squarefree modules

  • Tim Römer

Abstract:

In this paper we consider the category of squarefree modules over the polynomial ring and an exact duality functor, which is an extension of the Alexander dual of a simplicial complex. We give a relationship between the squarefree components of local cohomology groups of a squarefree module and the Tor groups of its dual. With this result it is shown that a squarefree module is sequentially Cohen–Macaulay if and only if the dual is componentwise linear.

Mathematics Subject Classification (2000): 13C14, 13D99 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Tim Römer
    • 1
  1. 1.FB 6, Mathematik und Informatik, Universität GH-Essen, 45117 Essen, Germany.¶e-mail: tim.roemer@uni-essen.deDE

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