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September 2005 A Second Main Theorem on Parabolic Manifolds
Min Ru, Julie Tzu-Yueh Wang
Asian J. Math. 9(3): 349-372 (September 2005).


In [St], [WS], Stoll and Wong-Stoll established the Second Main Theorem of meromorphic maps $f: M \rightarrow {\Bbb P}^N({\Bbb C})$ intersecting hyperplanes, under the assumption that $f$ is linear non-degenerate, where $M$ is a $m$-dimensional affine algebraic manifold(the proof actually works for more general category of Stein parabolic manifolds). This paper deals with the degenerate case. Using P. Vojta's method, we show that there exists a finite union of proper linear subspaces of ${\Bbb P}^N({\Bbb C})$, depending only on the given hyperplanes, such that for every (possibly degenerate) meromorphic map $f: M \rightarrow {\Bbb P}^N({\Bbb C})$, if its image is not contained in that union, the inequality of Wong-Stoll's theorem still holds (without the ramification term). We also carefully examine the error terms appearing in the inequality.


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Min Ru. Julie Tzu-Yueh Wang . "A Second Main Theorem on Parabolic Manifolds." Asian J. Math. 9 (3) 349 - 372, September 2005.


Published: September 2005
First available in Project Euclid: 3 May 2006

zbMATH: 1101.32007
MathSciNet: MR2214957

Rights: Copyright © 2005 International Press of Boston


Vol.9 • No. 3 • September 2005
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