Entire Curves in Algebraic Varieties

  • Junjiro Noguchi
  • Jörg Winkelmann
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 350)


In Chap.  3 the Second Main Theorem for differentiably non-degenerate meromorphic mappings f:C m V into a projective algebraic manifold V of dimVm was established in a satisfactory form. It is the next problem to deal with the case of m<dimV. In this case the freeness of the images inside V is very large, and causes the difficulties. It is still an open problem to establish the general Second Main Theorem in the case of m<dimV. We take the typical case of m=1 in this chapter. In the first half we will show the Cartan–Nochka Second Main Theorem for V=P n (C). The readers who first learn the theory of holomorphic curves in P n (C) should skip Sect. 4.1 and are recommended to read Sect. 4.2, assuming that holomorphic curves are linearly non-degenerate and the given hyperplanes are in general position; in this case, N=n, ω(j)=1, and \(\tilde{\omega}=1\).


Meromorphic Function Complex Manifold Holomorphic Curve Weighted Degree Entire Curve 
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Copyright information

© Springer Japan 2014

Authors and Affiliations

  • Junjiro Noguchi
    • 1
    • 2
  • Jörg Winkelmann
    • 3
  1. 1.The University of TokyoTokyoJapan
  2. 2.Tokyo Institute of TechnologyTokyoJapan
  3. 3.Ruhr-University BochumBochumGermany

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