On a Generating Curve of an Abelian Variety

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In his book "Varietes Abeliennes et Courbes Algebriques", A. Weil has proved that every Abelian Variety is generated by a finite number of Curves (cf.prop.30, § IX of the book). We shall show in this paper that every Abelian Variety is generated by one Curve. This will be one of basic tools for the investigation of Abelian Varieties. Using this, and applying Chow's result on Jacobian Varieties, we shall generalize his celebrated theorem to arbitrary Abelian Varieties in the forth-coming paper.

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