Journal Articles Épijournal de Géométrie Algébrique Year : 2023

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 special test configurations for polarizations close to the anticanonical bundle.

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Dates and versions

hal-02938823 , version 1 (15-09-2020)
hal-02938823 , version 2 (22-08-2022)

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Thibaut Delcroix. Uniform K-stability of polarized spherical varieties. Épijournal de Géométrie Algébrique, 2023, 7, ⟨10.46298/epiga.2022.9959⟩. ⟨hal-02938823v2⟩
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