On the cone of curves of an abelian variety

Original · EN

Let X be a smooth projective variety over the complex numbers. One knows by the Cone Theorem that the closed cone of curves of X is rational polyhedral whenever c₁(X) is ample. For varieties X such that c₁(X) is not ample, however, it is in general difficult to determine the structure of NE(X). The purpose of this paper is to study the cone of curves of abelian varieties. Specifically, the abelian varieties X are determined such that the closed cone NE(X) is rational polyhedral. The result can also be formulated in terms of the nef cone of X or in terms of the semi-group of effective classes in the Néron-Severi group of X.