On the Nochka-Chen-Ru-Wong Proof of Cartan's Conjecture

Details On the Nochka-Chen-Ru-Wong Proof of Cartan's Conjecture On the Nochka-Chen-Ru-Wong Proof of Cartan's Conjecture

2005-11-17

arxiv.org/abs/math/0511459v2

Journal of Number Theory 125 (2007), pp. 229-234

Mathematics

Number Theory

6 pages, 1 figure. Reorganized to reflect the submitted version; added a reference to a paper of Nochka

Scientific paper

10.1016/j.jnt.2006.10.014

In 1982-83, E. Nochka proved a conjecture of Cartan on defects of holomorphic curves in $\Bbb P^n$ relative to a possibly degenerate set of hyperplanes. This was further explained by W. Chen in his 1987 thesis, and subseqently simplified by M. Ru and P.-M. Wong in 1991. The proof involved assigning weights to the hyperplanes. This paper provides a mild simplification of the proof of the construction of the weights, by construing the ``Nochka diagram'' of Ru and Wong as a convex hull.

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