On the irreducible components of moduli schemes for affine spherical varieties

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 ${\mathrm{M}}_{\Gamma }$.

v4: 26 pages, final version

References in corpus (6)

• Wonderful Varieties: A geometrical realization
• Invariant Hilbert schemes
• New and old results on spherical varieties via moduli theory
• Primitive wonderful varieties
• The moduli scheme of affine spherical varieties with a free weight monoid
• Equivariant degenerations of spherical modules for groups of type A

Cited by in corpus (5)

• New and old results on spherical varieties via moduli theory
• The moduli scheme of affine spherical varieties with a free weight monoid
• Root subgroups on affine spherical varieties
• Equivariant degenerations of spherical modules: part II
• Momentum polytopes of projective spherical varieties and related Kähler geometry