The moduli scheme of affine spherical varieties with a free weight monoid

Abstract

We study Alexeev and Brion's moduli scheme $M_{\Gamma }$ of affine spherical varieties with weight monoid $\Gamma$ under the assumption that $\Gamma$ is free. We describe the tangent space to $M_{\Gamma }$ at its `most degenerate point' in terms of the combinatorial invariants of spherical varieties and deduce that the irreducible components of $M_{\Gamma }$, equipped with their reduced induced scheme structure, are affine spaces.

v1: 26 pages. v2: 27 pages, improved exposition. v3: 27 pages, Corollary 4.3 removed due to error in proof, other results unaffected, new Remark 5.5, scheme structure made explicit. v4: 29 pages, implemented changes requested by referee

References in corpus (6)

• Wonderful Varieties: A geometrical realization
• An introduction to wonderful varieties with many examples of type F4
• Homogeneous spaces and equivariant embeddings
• Equivariant degenerations of spherical modules for groups of type A
• On the irreducible components of moduli schemes for affine spherical varieties
• Equivariant degenerations of spherical modules: part II

Cited by in corpus (4)

• New and old results on spherical varieties via moduli theory
• On the irreducible components of moduli schemes for affine spherical varieties
• Root subgroups on affine spherical varieties
• Equivariant degenerations of spherical modules: part II