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.
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Received: 7 June 1999 / Revised version: 6 September 2000
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Römer, T. Cohen–Macaulayness and squarefree modules. manuscripta math. 104, 39–48 (2001). https://doi.org/10.1007/s002290170045
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DOI: https://doi.org/10.1007/s002290170045