Defects for Ample Divisors of Abelian Varieties, Schwarz Lemma, and Hyperbolic Hypersurfaces of Low Degrees

Details Defects for Ample Divisors of Abelian Varieties, Schwarz Lemma, and Hyperbolic Hypersurfaces of Low Degrees Defects for Ample Divisors of Abelian Varieties, Schwarz Lemma, and Hyperbolic Hypersurfaces of Low Degrees

1996-10-14

arxiv.org/abs/math/9610203v1

Mathematics

Complex Variables

Scientific paper

The main purpose of this paper is to prove the following theorem on the defect relations for ample divisors of abelian varieties. Main Theorem. Let $A$ be an abelian variety of complex dimension $n$ and $D$ be an ample divisor in $A$. Let $f:{\bf C}\rightarrow A$ be a holomorphic map. Then the defect for the map $f$ and the divisor $D$ is zero. Corollary to Main Theorem. The complement of an ample divisor $D$ in an abelian variety $A$ is hyperbolic in the sense that there is no nonconstant holomorphic map from $\bf C$ to $A-D$.

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