Northwestern-UIC Complex Geometry Seminar

Abstract: 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. This is joint work with Kewei Zhang.

In the course of studying problems related to Kahler-Einstein type metrics, a key step is to show they form a compact space. We would like to discuss an algebraic approach which gives a unified treatment of the all these problems, in the level of varying the underlying algebraic structures. The strategy can be divided into two steps. We will focus on the second step, where the main recipe is a new type of finite generation results.