Affiliation:
1. Department of Mathematics University of Maryland College Park Maryland USA
2. School of Mathematical Sciences Beijing Normal University Beijing China
Abstract
AbstractWe prove existence of twisted Kähler–Einstein metrics in big cohomology classes, using a divisorial stability condition. In particular, when is big, we obtain a uniform Yau–Tian–Donaldson (YTD) existence theorem for Kähler–Einstein (KE) 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 YTD existence theorems for KE 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.
Funder
Alfred P. Sloan Foundation
National Science Foundation
National Natural Science Foundation of China
Fundamental Research Funds for the Central Universities