论文标题
大班扭曲的Kähler-Einstein指标
Twisted Kähler-Einstein metrics in big classes
论文作者
论文摘要
我们证明了使用分区稳定性条件在大共同体学类中证明了扭曲的Kähler-Einstein指标。特别是，当$ -K_X $很大时，我们获得了Kähler-Einstein指标的统一Yau-Tian-Donaldson存在定理。为了实现这一目标，我们使用多能理论从头开始在先验大环境中建立了藤田 - 奥达卡类型不变的理论。我们在论点中不使用K能量，并且我们的技术提供了一个简单的路线图来证明Yau-tian-Donaldson的存在定理，用于Kähler-Einstein型指标，只需要适当的ding能量的凸度。作为一个应用程序，我们在日志Fano设置中简化了Li-Tian-Wang的存在定理证明。
We prove existence of twisted Kähler-Einstein metrics in big cohomology classes, using a divisorial stability condition. In particular, when $-K_X$ is big, we obtain a uniform Yau-Tian-Donaldson existence theorem for Kähler-Einstein metrics. To achieve this, we build up from scratch the theory of Fujita-Odaka type delta invariants in the transcendental big setting, using pluripotential theory. We do not use the K-energy in our arguments, and our techniques provide a simple roadmap to prove Yau-Tian-Donaldson existence theorems for Kähler-Einstein type metrics, that only needs convexity of the appropriate Ding energy. As an application, we give a simplified proof of Li-Tian-Wang's existence theorem in the log Fano setting.
