Elliptic curves on abelian varieties (Q281487)

To find elliptic curves on abelian varieties is an interesting problem. In the present paper, the author gives a characterization of all elliptic curves on an abelian variety in terms of the structure of its Neron-Severi group. Precisely, the author proves that an abelian variety \(A\) over an algebraic closed field contains an elliptic curve if and only if there exists \(0\not=\alpha\in\mathrm{NS}(A)\) such that \(\alpha^2=0\).