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摘要翻译：
1941年，L.Ahlfors给出了H.Cartan关于P^n中全纯曲线逼近超平面的1933年定理的另一个证明。Ahlfors的证明建立在H.和J.Weyl(1938)早期工作的基础上，通过研究全纯曲线的关联曲线证明了Cartan定理。这项工作随后由H.-H.重新编写。吴于1970年利用微分几何，M.Cowen和P.A.Griffiths于1976年进一步强调曲率，并由Y.-T.Siu在1987年和1990年，强调亚纯连接。本文以Schmidt子空间定理证明中的连续极小值为动力，利用McQuillan的“重言式不等式”，给出了该证明的另一种变体。在这个证明中，基本上所有的分析都被封装在一个修正的类McQuillan不等式中，因此大多数证明主要使用代数几何的方法，特别是标志变体。提出了一个基于McQuillan不等式的diophantine猜想。
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英文标题：
《On McQuillan's "tautological inequality" and the Weyl-Ahlfors theory of
associated curves》
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作者：
Paul Vojta
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Complex Variables 复变数
分类描述：Holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves
全纯函数，自守群作用与形式，伪凸性，复几何，解析空间，解析束
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一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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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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PDF链接：
https://arxiv.org/pdf/0706.3044
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