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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