On the cone of curves of an abelian variety

Details On the cone of curves of an abelian variety On the cone of curves of an abelian variety

1997-12-17

arxiv.org/abs/alg-geom/9712019v1

Mathematics

Algebraic Geometry

Scientific paper

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 $c_1(X)$ is ample. For varieties $X$ such that $c_1(X)$ is not ample, however, it is in general difficult to determine the structure of $\bar NE(X)$. 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 $\bar NE(X)$ 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 N\'eron-Severi group of $X$.

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