丘成桐-田刚-唐纳森猜想的反证
Disproof of the Yau--Tian--Donaldson conjecture
AI总结：
本文构造了一个K-多稳定但无对应常数量曲率凯勒度量的极化光滑射影五维流形，借助生成式AI完成核心结果，反证了丘成桐-田刚-唐纳森猜想。
AI中文摘要：
我们构造了一个极化光滑射影五维流形，证明其为K-多稳定但不允许常数量曲率凯勒度量，这反证了关于常数量曲率度量的丘成桐-田刚-唐纳森猜想。本文主要结果借助生成式AI得到，具体包括GPT-5.6-sol、Fable 5及Danus系统，关于生成式AI使用的详细报告随附录一同附出，合作者为董斌和高国雄。
英文摘要：
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.
