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arXiv · 2208.08324

Twisted K\"ahler-Einstein metrics in big classes

Tamás Darvas·Kewei Zhang
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Abstract

We prove existence of twisted K\"ahler-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 K\"ahler-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 K\"ahler-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.

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Tamás Darvas, Kewei Zhang. 2022-08-17. Twisted K\"ahler-Einstein metrics in big classes. https://arxiv.org/abs/2208.08324

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