Bounds for Curves in Abelian Varieties

Details Bounds for Curves in Abelian Varieties Bounds for Curves in Abelian Varieties

2002-07-17

arxiv.org/abs/math/0207139v3

Mathematics

Algebraic Geometry

24 pages, LaTeX; minor corrections

Scientific paper

A uniform bound of intersection multiplicities of curves and divisors on abelian varieties is proved by algebraic geometric methods. It extends and improves a result obtained by A. Buium with a different method based on Kolchin's differential algebra. The problem is modeled after the abc-Conjecture of Masser-Oesterle for abelian varieties over the function field of a curve. As an application a finiteness theorem is proved for maps from a curve into an abelian variety omitting an ample divisor.

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