The Second Main Theorem for Holomorphic Curves into Semi-Abelian Varieties II

Junjiro Noguchi; Jörg Winkelmann; Katsutoshi Yamanoi

The Second Main Theorem for Holomorphic Curves into Semi-Abelian Varieties II

Complex Variables 2007-05-23 v2 Algebraic Geometry

Authors: Junjiro Noguchi , Jörg Winkelmann , Katsutoshi Yamanoi

Abstract

We establish the second main theorem with the best truncation level one for an entire holomorphic curve $f:\C \to A$ into a semi-abelian variety $A$ and an arbitrary effective reduced divisor $D$ on $A$ ; the low truncation level is important for applications. We will actually prove this for the jet lifts of $f$ . Finally we give some applications, including the solution of a problem posed by Mark Green.

Keywords

algebraic curves abelian varieties hyperelliptic curves

Cite

@article{arxiv.math/0405492,
  title  = {The Second Main Theorem for Holomorphic Curves into Semi-Abelian Varieties II},
  author = {Junjiro Noguchi and Jörg Winkelmann and Katsutoshi Yamanoi},
  journal= {arXiv preprint arXiv:math/0405492},
  year   = {2007}
}

Comments

37 pages, LaTeX. In this version the Main theorem has been generalized: Now D may be a subvariety of any codimension and need not be a divisor

The Second Main Theorem for Holomorphic Curves into Semi-Abelian Varieties II

Abstract

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