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

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

1999-12-10

arxiv.org/abs/math/9912086v2

Mathematics

Complex Variables

LaTeX, 37 pages

Scientific paper

10.1016/S0764-4442(00)01614-1

Let f:C -> A be an entire holomorphic curve into a semi-Abelian variety A.
Then the Zariski closure of f(C) is a translate of a semi-Abelian subvariety of
A (logarithmic Bloch-Ochiai's theorem). The purpose of the present paper is to
establish a quantitative version of the above result for such f i.e., the
second main theorem and the defect relation.

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