关于McQuillan的“重言式不等式”和相伴曲线的Weyl-Ahlfors理论
On McQuillan's "tautological inequality" and the Weyl-Ahlfors theory of associated curves
摘要：
1941年，L. Ahlfors给出了另一个证明1933年定理H。P^n中全纯曲线超平面的Cartan逼近Ahlfors的证明建立在H.和J. Weyl（1938），并通过研究全纯曲线的相关曲线证明了Cartan定理。这项工作后来由H. H. 1970年，M. Cowen和P.A. Griffiths在1976年进一步强调了曲率，Y. T. Siu在1987年和1990年提出的，强调亚纯联络。本文利用Schmidt子空间定理证明中的连续极小值，并利用McQuillan的重言式不等式，给出了证明的另一种变形。在这个证明中，基本上所有的分析都被封装在一个修改的McQuillan不等式中，因此大多数证明主要使用代数几何的方法，特别是标志种类。基于McQuillan不等式提出了一个丢番图猜想。
英文摘要：
In 1941, L. Ahlfors gave another proof of a 1933 theorem of H. Cartan on approximation to hyperplanes of holomorphic curves in P^n. Ahlfors' proof built on earlier work of H. and J. Weyl (1938), and proved Cartan's theorem by studying the associated curves of the holomorphic curve. This work has subsequently been reworked by H.-H. Wu in 1970, using differential geometry, M. Cowen and P. A. Griffiths in 1976, further emphasizing curvature, and by Y.-T. Siu in 1987 and 1990, emphasizing meromorphic connections. This paper gives another variation of the proof, motivated by successive minima as in the proof of Schmidt's Subspace Theorem, and using McQuillan's "tautological inequality." In this proof, essentially all of the analysis is encapsulated within a modified McQuillan-like inequality, so that most of the proof primarily uses methods of algebraic geometry, in particular flag varieties. A diophantine conjecture based on McQuillan's inequality is also posed.
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