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Entire Curves in Semi-abelian Varieties

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

Abstract

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.

Keywords

Algebraic Variety Abelian Variety Ideal Sheaf Zariski Closure Ample Divisor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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