= Solution
The <Nakai–Moishezon criterion> says that a <Cartier divisor> $D$ on a <projective scheme> is <ample> exactly when
$$
D^{\dim Y}\cdot Y>0
$$
for every positive-dimensional integral closed <subvariety> $Y$. <Kleiman's criterion> says that the <ample cone> is the interior of the <nef cone>; equivalently, the <numerical class> of $D$ is ample exactly when it is strictly positive on every nonzero element of the <closed cone of curves> $\overline{\operatorname{NE}}(X)$. Positivity merely on individual curves is insufficient: the closure of the cone is essential. A <nef divisor> has nonnegative <intersection number> with every integral curve, and its restriction to every closed subscheme is nef.
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