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ON THE IRREDUCIBLE COMPONENTS OF MODULI SCHEMES FOR AFFINE SPHERICAL VARIETIES

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Abstract

We give a combinatorial description of all affine spherical varieties with prescribed weight monoid Г. As an application, we obtain a characterization of the irreducible components of Alexeev and Brion’s moduli scheme MГ for such varieties. Moreover, we find several sufficient conditions for MГ to be irreducible and exhibit several examples where MГ is reducible. Finally, we provide examples of non-reduced MГ.

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Authors and Affiliations

  1. Higher School of Economics, National Research University, Moscow, Russia

    ROMAN AVDEEV

  2. Ruhr-Universität Bochum, NA 4/67, D-44797, Bochum, Germany

    STÉPHANIE CUPIT-FOUTOU

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  1. ROMAN AVDEEV
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  2. STÉPHANIE CUPIT-FOUTOU
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Correspondence to ROMAN AVDEEV.

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AVDEEV, R., CUPIT-FOUTOU, S. ON THE IRREDUCIBLE COMPONENTS OF MODULI SCHEMES FOR AFFINE SPHERICAL VARIETIES. Transformation Groups 23, 299–327 (2018). https://doi.org/10.1007/s00031-017-9443-8

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