The uniform version of Yau-Tian-Donaldson conjecture for singular Fano varieties

Abstract

We prove the following result: if a $\mathbb{Q}$-Fano variety is uniformly K-stable, then it admits a Kähler-Einstein metric. We achieve this by modifying Berman-Boucksom-Jonsson's strategy with appropriate perturbative arguments and non-Archimedean estimates. The idea of using the perturbation is motivated by our previous paper.

arXiv comment36 pages. Add more details according to the referee's request. Comments Welcome

References in corpus (3)

• Tian's properness conjectures and Finsler geometry of the space of Kahler metrics
• A non-Archimedean approach to K-stability
• On the Yau-Tian-Donaldson conjecture for singular Fano varieties

Cited by in corpus (9)

• K-stability of Fano varieties: an algebro-geometric approach
• A quantization proof of the uniform Yau-Tian-Donaldson conjecture
• Product theorem for K-stability
• On K-stability of some del Pezzo surfaces of Fano index 2
• Equivariant K-stability under finite group action
• Openness of uniform K-stability in the Kähler cone
• A decomposition theorem for $\mathbb{Q}$-Fano Kähler-Einstein varieties
• Valuative invariants with higher moments
• On K-stability of Fano weighted hypersurfaces