Twisted Kähler-Einstein metrics in big classes

2022/08/17 by Tamás Darvas, Kewei Zhang, Darvas, Tamás +1 · 4 citations
Mathematics · #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2208.08324

openalex publication_date 2022/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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. 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 Kähler-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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Related

• Stability thresholds for big classes
• Continuity of delta invariants and twisted Kähler--Einstein metrics
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