论文标题
Kähler-Ricci流量限制和最佳变种的代数唯一性
Algebraic uniqueness of Kähler-Ricci flow limits and optimal degenerations of Fano varieties
论文作者
论文摘要
我们证明，对于任何$ \ mathbb {q} $ - fano variety $ x $，特殊$ \ mathbb {r} $ - 测试配置最小化$ h $ - 功能是唯一的，并且具有k的$ \ mathbb {q} Q} $ - fano central fiber fiber fiber $（w，w，w，ξ）$。此外，$（w，ξ）$的唯一k-polystable变性。作为一种应用，我们确认了Chen-sun-wang关于Kähler-Icci流动流量限制的代数唯一性的猜想，这意味着该流量的Gromov-Hausdorff限制并不取决于初始Kähler量级的选择。结果是通过研究代数最佳变性问题通过新的估值功能来实现的，这些功能类似于归一化体积的最小化问题。
We prove that for any $\mathbb{Q}$-Fano variety $X$, the special $\mathbb{R}$-test configuration that minimizes the $H$-functional is unique and has a K-semistable $\mathbb{Q}$-Fano central fibre $(W, ξ)$. Moreover there is a unique K-polystable degeneration of $(W, ξ)$. As an application, we confirm the conjecture of Chen-Sun-Wang about the algebraic-uniqueness for Kähler-Ricci flow limits on Fano manifolds, which implies that the Gromov-Hausdorff limit of the flow does not depend on the choice of initial Kähler metrics. The results are achieved by studying algebraic optimal degeneration problems via new functionals of real valuations, which are analogous to the minimization problem for normalized volumes.
