On the irreducible components of moduli schemes for affine spherical varieties

Roman Avdeev; Stéphanie Cupit-Foutou

doi:10.1007/s00031-017-9443-8

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arXiv · 1406.1713

On the irreducible components of moduli schemes for affine spherical varieties

Roman Avdeev·Stéphanie Cupit-Foutou

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Abstract

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

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Roman Avdeev, Stéphanie Cupit-Foutou. 2014-06-06. On the irreducible components of moduli schemes for affine spherical varieties. https://doi.org/10.1007/s00031-017-9443-8

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