论文标题
Yau-tian-Donaldson构想的同一性一个歧管
The Yau-Tian-Donaldson conjecture for cohomogeneity one manifolds
论文作者
论文摘要
我们证明了Yau-tian-Donaldson对同一歧管的猜想，也就是说，对于配备有一个至少一个真实的超脸轨道的紧凑型谎言组的投射歧管。与似乎是一种普遍的看法相反，这种流派并未承认在所有Kähler课程中的极端Kähler指标。更普遍地，我们证明，对于一种极化的球形品种，G-均匀K稳定性相当于K稳定性相对于特殊的G-均衡测试构型。此外，这是由单个组合条件编码的，在实践中可检查。我们说明了示例，并回答了Kanemitsu的问题。
We prove the Yau-Tian-Donaldson conjecture for cohomogeneity one manifolds, that is, for projective manifolds equipped with a holomorphic action of a compact Lie group with at least one real hypersurface orbit. Contrary to what seems to be a popular belief, such manifolds do not admit extremal Kähler metrics in all Kähler classes in general. More generally, we prove that for rank one polarized spherical varieties, G-uniform K-stability is equivalent to K-stability with respect to special G-equivariant test configurations. This is furthermore encoded by a single combinatorial condition, checkable in practice. We illustrate on examples and answer along the way a question of Kanemitsu.
