The Luna-Vust Theory of Spherical Embeddings

By F. Knop. 2012

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Primitive wonderful varieties (2011, methodology): “], [4]. In this paper we complete the proof of the Luna conjecture along the lines of this program. Thanks to [19, Theorem 2] and the Luna-Vust theory of embeddings of sphericalhomogeneousspaces (see [13]), this completes the classiﬁcationof spherical varieties, i.e. normal G-varieties where a Borel”
The Spherical Systems of the Wonderful Reductive Subgroups (2011, unknown): “On one hand, the abstract spherical systems that can be associated with a wonderful reductive subgroup are classiﬁed: this comes from the combinatorial study of all the abstract spherical systems of [4] and a criterion for reductivity due to Knop [15].”
K-stability of Fano spherical varieties (2016, methodology): “ant automorphisms of a spherical variety X is isomorphic to the neutral component of the group of G-equivariant automorphisms of its open G-orbit, through the restriction. Indeed, the construction in [Kno91] of the colored fan FX of a spherical embedding (X,x) of G/Hdoes not depend on the choice of ”