Uniform K-stability of polarized spherical varieties

Abstract

We express notions of K-stability of polarized spherical varieties in terms of combinatorial data, vastly generalizing the case of toric varieties. We then provide a combinatorial sufficient condition of G-uniform K-stability by studying the corresponding convex geometric problem. Thanks to recent work of Chi Li and a remark by Yuji Odaka, this provides an explicitly checkable sufficient condition of existence of constant scalar curvature Kahler metrics. As a side effect, we show that, on several families of spherical varieties, G-uniform K-stability is equivalent to K-polystability with respect to G-equivariant test configurations for polarizations close to the anticanonical bundle.

with an appendix by Yuji Odaka, v2 taking into account referee's comments and correcting minor mistakes, v3 EPIGA journal version

References in corpus (4)

• On the constant scalar curvature Kähler metrics, existence results
• On the constant scalar curvature Kähler metrics, general automorphism group
• Geodesic rays and stability in the cscK problem
• Examples of K-unstable Fano manifolds

Cited by in corpus (4)

• The Yau-Tian-Donaldson conjecture for cohomogeneity one manifolds
• An effective weighted K-stability condition for polytopes and semisimple principal toric fibratons
• Openness of uniform K-stability in the Kähler cone
• K-stability and polystable degenerations of polarized spherical varieties