论文标题
两极分化的统一K稳定性
Uniform K-stability of polarized spherical varieties
论文作者
论文摘要
我们在组合数据方面表达了极化球形品种的K稳定性概念，从而极大地概括了复曲面品种的情况。然后，我们通过研究相应的凸几何问题来提供G-均匀K稳定性的足够组合条件。得益于Chi Li的最新工作以及Yuji Odaka的言论，这提供了明确可检查的足够的足够条件。作为副作用，我们表明，对于几个球形品种的家族，G-均匀的K稳定性等于K-溶解度相当于G-均衡性测试构型，用于接近反典型束的极化。
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.
