Disproof of the Yau--Tian--Donaldson conjecture

Abstract

We construct a polarized smooth projective fivefold and prove that it is K-polystable but does not admit a constant scalar curvature Kähler metric. This disproves the Yau--Tian--Donaldson conjecture for constant scalar curvature metrics. The main result of this paper was obtained using generative AI, particularly GPT-5.6-sol, Fable 5, and the Danus system. A detailed report on the use of generative AI in this paper is enclosed in the appendix, joint with Bin Dong and Guoxiong Gao.

79 pages. Main result of this paper obtained by generative AI. Including an appendix joint with Bin Dong and Guoxiong Gao as a detailed report on the use of generative AI in this paper