Entire Curves in Semi-abelian Varieties

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


The value distribution of entire curves f from C into semi-abelian varieties A is studied here. We first study the order functions and the structure of the Zariski closures of their jet images J k (f)(C). Then we will prove the Second Main Theorem for J k (f),k≧0. For better understanding we begin with the simplest case where A is compact. Then we will prove the Second Main Theorem in the case of semi-abelian A with counting functions \(N_{k_{0}}(r, f^{*}D)\). Making use of these results we finally establish the Second Main Theorem for J k (f) with counting functions truncated to level one; this is the best case.

The Second Main Theorem with truncation level one has a number of interesting applications; in particular, we will apply it to the algebraic degeneracy problem for entire curves into algebraic varieties.


Algebraic Variety Abelian Variety Ideal Sheaf Zariski Closure Ample Divisor 
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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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