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In 1941, L. Ahlfors gave another proof of a 1933 theorem of H. Cartan onapproximation to hyperplanes of holomorphic curves in P^n. Ahlfors' proof builton earlier work of H. and J. Weyl (1938), and proved Cartan's theorem bystudying the associated curves of the holomorphic curve. This work hassubsequently 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 givesanother variation of the proof, motivated by successive minima as in the proofof Schmidt's Subspace Theorem, and using McQuillan's "tautological inequality."In this proof, essentially all of the analysis is encapsulated within amodified McQuillan-like inequality, so that most of the proof primarily usesmethods of algebraic geometry, in particular flag varieties. A diophantineconjecture based on McQuillan's inequality is also posed.

On McQuillan's "tautological inequality" and the Weyl-Ahlfors theory of associated curves