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Bounds for Curves in Abelian Varieties

Junjiro Noguchi·Joerg Winkelmann
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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.

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Junjiro Noguchi, Joerg Winkelmann. 2002-08-12. Bounds for Curves in Abelian Varieties. https://arxiv.org/abs/math/0207139

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