Existence of twisted Kahler-Einstein metrics in big classes

Existence of twisted Kahler-Einstein metrics in big classes

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Tamás Darvas, University of Maryland
Fine Hall 314

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.