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Non-normal affine monoid algebras

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Abstract

We give a geometric description of the set of holes in a non-normal affine monoid Q. The set of holes turns out to be related to the non-trivial graded components of the local cohomology of \({\mathbb{K}[Q]}\). From this, we see how various properties of \({\mathbb{K}[Q]}\) like local normality and Serre’s conditions (R 1) and (S 2) are encoded in the geometry of the holes. A combinatorial upper bound for the depth the monoid algebra \({\mathbb{K}[Q]}\) is obtained which in some cases can be used to compute its depth.

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Authors and Affiliations

  1. FB Mathematik/Informatik, Universität Osnabrück, 49069, Osnabrück, Germany

    Lukas Katthän

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  1. Lukas Katthän
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Correspondence to Lukas Katthän.

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This work was supported by the DAAD.

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Katthän, L. Non-normal affine monoid algebras. manuscripta math. 146, 223–233 (2015). https://doi.org/10.1007/s00229-014-0685-7

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  • DOI: https://doi.org/10.1007/s00229-014-0685-7

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