Thibaut Delcroix - Uniform K-stability of polarized spherical varieties

epiga:9959 - Épijournal de Géométrie Algébrique, March 23, 2023, Volume 7 - https://doi.org/10.46298/epiga.2022.9959
Uniform K-stability of polarized spherical varietiesArticle

Authors: Thibaut Delcroix

    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.


    Volume: Volume 7
    Published on: March 23, 2023
    Accepted on: December 1, 2022
    Submitted on: August 24, 2022
    Keywords: Mathematics - Algebraic Geometry,Mathematics - Complex Variables,Mathematics - Differential Geometry,14M27, 32Q26, 53C25, 32Q20
    Funding:
      Source : OpenAIRE Graph
    • Fibrations and algebraic group actions; Funder: French National Research Agency (ANR); Code: ANR-18-CE40-0003
    • Real Monge-Ampère and Kähler geometry of homogeneous spaces; Funder: French National Research Agency (ANR); Code: ANR-21-CE40-0011

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