Bounds for Curves in Abelian Varieties
Algebraic Geometry
2007-05-23 v3 Complex Variables
Abstract
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.
Cite
@article{arxiv.math/0207139,
title = {Bounds for Curves in Abelian Varieties},
author = {Junjiro Noguchi and Joerg Winkelmann},
journal= {arXiv preprint arXiv:math/0207139},
year = {2007}
}
Comments
24 pages, LaTeX; minor corrections