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Isotropic subspaces of Orlik-Solomon algebras

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Abstract

We give a combinatorial characterization of isotropic subspaces in the Orlik-Solomon algebra of a hyperplane arrangement in terms of decorations of its intersection lattice. We then use this characterization to prove a result that relates these isotropic subspaces with linear systems supported on the arrangement, for arrangements with isolated non-normal crossings of a particular form.

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Authors and Affiliations

  1. Centro Universitario de la Defensa, Academia General Militar, Carretera de Huesca S/N, Zaragoza, Spain

    Miguel A. Marco-Buzunáriz

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  1. Miguel A. Marco-Buzunáriz
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Correspondence to Miguel A. Marco-Buzunáriz.

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Research partially supported by the ERC Starting Grant project TGASS and by Spanish Contract MTM2007-67908-C02-02. The author thanks to the Facultad de Ciencias Matemáticas of the Universidad Complutense de Madrid and the Universidad de Zaragoza for excellent working conditions.

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Marco-Buzunáriz, M.A. Isotropic subspaces of Orlik-Solomon algebras. Rev Mat Complut 24, 527–538 (2011). https://doi.org/10.1007/s13163-010-0052-5

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  • DOI: https://doi.org/10.1007/s13163-010-0052-5

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