发表机构
Academy of Mathematics and Systems Science, Chinese Academy of Sciences; State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences; School of Mathematical Sciences, University of Chinese Academy of Sciences（中国科学院数学与系统科学研究院; 中国科学院数学与系统科学研究院数学科学国家重点实验室; 中国科学院大学数学科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过射流技术给出Miyaoka--Mori判据的代数证明，构造通过负典范曲线上任意点的有理曲线，并结合BDPP锥对偶性恢复射影无理性判据。
AI 中文摘要
我们在特征零情形下给出了Miyaoka--Mori判据的代数证明：光滑射影簇上典范次数为负的曲线上的每一点都位于一条有理曲线上。我们的射流技术还给出了原曲线类的一个有效数值分解。对于每个指定点，该分解包含一条通过该点的有理曲线，其系数为正且与点无关，反典范次数至多为$\dim X+1$。结合BDPP锥对偶性，这恢复了在$\mathbb C$上的射影无理性判据。本文的主要结果是使用Pharos系统获得的。关于Pharos的使用以及主要论证的Lean~4形式化的详细报告见附录B，由Bin Dong、Guoxiong Gao、Zeming Sun和Bin Wu撰写。
英文摘要
We give an algebraic proof in characteristic zero of the Miyaoka--Mori criterion: every point of a curve of negative canonical degree on a smooth projective variety lies on a rational curve. Our jet technique gives, in addition, an effective numerical decomposition of the original curve class. For each prescribed point, the decomposition contains a rational curve through that point, with a positive coefficient independent of the point and with anticanonical degree at most $\dim X+1$. Together with BDPP cone duality, this recovers the projective uniruledness criterion over $\mathbb C$. The main result of this paper was obtained using the Pharos system. A detailed report on the use of Pharos and on the Lean~4 formalization of the main arguments is given in the Appendix B, written by Bin Dong, Guoxiong Gao, Zeming Sun, and Bin Wu.
