Elliptic curves on abelian surfaces
Elliptic curves on abelian surfaces
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阿贝尔曲面上的椭圆曲线
DOI：
10.1007/bf02567454
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发表时间：
1994
影响因子：
0.6
通讯作者：
E. Kani
中科院分区：
文献类型：
--
作者：
E. Kani
本文的目的是提出两个定理，概述阿贝尔曲面上的椭圆曲线集，并讨论几种应用。这些应用之一是 Biermann (1883) 和 Humbert (1893) 的经典定理，该定理根据 Humbert 的“奇异关系”来表征包含椭圆曲线的阿贝尔曲面。作为副产品，人们获得了这种关系的纯代数描述，因此也获得了亨伯特曲面的纯代数描述。
The purpose of this paper is to present two theorems which give an overview of the set of elliptic curves lying on an abelian surface and to discuss several applications. One of these applications is a classical theorem of Biermann (1883) and Humbert (1893) on the characterization of abelian surfaces containing elliptic curves in terms of the “singular relations” of Humbert. As a by-product one obtains a purely algebraic description of such relations and hence also ofHumbert surfaces.