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## On the irreducible components of moduli schemes for affine spherical varieties

Transformation Groups. 2018. Vol. 23. No. 2. P. 299-327.
Roman Avdeev, Cupit-Foutou S.

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