Geodesic
Uniform K-stability of polarized spherical varieties
Épijournal de Géométrie Algébrique, Tome 7 (2023)

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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.
DOI : 10.46298/epiga.2022.9959
Classification : 14M27, 32Q20, 32Q26, 53C25 
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     author = {Delcroix, Thibaut},
     title = {Uniform {K-stability} of polarized spherical varieties},
     journal = {\'Epijournal de G\'eom\'etrie Alg\'ebrique},
     publisher = {mathdoc},
     volume = {7},
     year = {2023},
     doi = {10.46298/epiga.2022.9959},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/epiga.2022.9959/}
}
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Delcroix, Thibaut. Uniform K-stability of polarized spherical varieties. Épijournal de Géométrie Algébrique, Tome 7 (2023). doi: 10.46298/epiga.2022.9959

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