论文标题
丁稳定性和Kähler-Einstein指标在具有大型抗宗教类别的流形上
Ding stability and Kähler-Einstein metrics on manifolds with big anticanonical class
论文作者
论文摘要
我们引入了一个均匀的ding稳定性的概念，该概念具有大型反典型类别的投射歧管，并证明存在独特的Kähler-Einstein指标上的这种歧管上的存在意味着统一的滴定稳定性。主要的新技术是为单数指标开发出deligne功能和相应斜率公式的一般理论，并证明在大环境中ding函数的斜率公式。这扩展了伯曼在Fano的情况下的工作，当时反典型的阶级实际上是足够的，并且证明了在这种情况下Yau-Tian-Donaldson的类似物的一个方向。我们还推测在大环境中均匀的丁字稳定性和K稳定性与模量的相关性。
We introduce a notion of uniform Ding stability for a projective manifold with big anticanonical class, and prove that the existence of a unique Kähler-Einstein metric on such a manifold implies uniform Ding stability. The main new techniques are to develop a general theory of Deligne functionals - and corresponding slope formulas - for singular metrics, and to prove a slope formula for the Ding functional in the big setting. This extends work of Berman in the Fano situation, when the anticanonical class is actually ample, and proves one direction of the analogue of the Yau-Tian-Donaldson conjecture in this setting. We also speculate about the relevance of uniform Ding stability and K-stability to moduli in the big setting.
