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arXiv · 2608.19301

Disproof of the Yau--Tian--Donaldson conjecture

Jihao Liu
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Abstract

We construct a polarized smooth projective fivefold and prove that it is K-polystable but does not admit a constant scalar curvature K\"ahler 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.

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Jihao Liu. 2026-08-19. Disproof of the Yau--Tian--Donaldson conjecture. https://arxiv.org/abs/2608.19301

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