Bounds for Curves in Abelian Varieties
Bounds for Curves in Abelian Varieties
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DOI：
10.1515/crll.2004.052
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发表时间：
2002-07
期刊：
影响因子：
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通讯作者：
J. Noguchi;J. Winkelmann
中科院分区：
文献类型：
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作者：
J. Noguchi;J. Winkelmann
用代数几何方法证明了交换簇上曲线与因子的交重数的一致界。推广和改进了A. Buium与不同的方法的基础上Kolchin的微分代数。这个问题是仿照的Masser-Oesterle的阿贝尔簇的函数域上的曲线的abc-猜想。作为应用，证明了从曲线到阿贝尔簇的映射的一个有限性定理。
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.