Wonderful Varieties: A geometrical realization

Abstract

A geometrical realization of wonderful varieties by means of a suitable class of invariant Hilbert schemes is given. As a consequence, Luna's conjecture asserting that wonderful varieties are classified by spherical systems, triples of combinatorial invariants, is proved.

v2, 34 pages, major changes; v3 some gaps fixed; v4 53 pages, some details added

Cited by in corpus (21)

• Invariant Hilbert schemes
• On solvable spherical subgroups of semisimple algebraic groups
• New and old results on spherical varieties via moduli theory
• Orbits of strongly solvable spherical subgroups on the flag variety
• Primitive wonderful varieties
• The moduli scheme of affine spherical varieties with a free weight monoid
• On the irreducible components of moduli schemes for affine spherical varieties
• Equivariant degenerations of spherical modules for groups of type A
• Schémas de Hilbert invariants et théorie classique des invariants
• Wonderful varieties of type B and C
• Manin's conjecture for certain spherical threefolds
• Regular functions on spherical nilpotent orbits in complex symmetric pairs: classical non-Hermitian cases
• Satellites of spherical subgroups
• Wonderful subgroups of reductive groups and spherical systems
• Primitive spherical systems
• Characterizing quasi-affine spherical varieties via the automorphism group
• Degenerations of spherical subalgebras and spherical roots
• Containment Relations among Spherical Subgroups
• Invariant deformation theory of affine schemes with reductive group action
• Antiholomorphic involutions and spherical subgroups of reductive groups
• Spherical subgroups of Kac-Moody groups and transitive actions on spherical varieties