Let $X$ be a K3 surface over $\mathbb{C}$. On a $K3$ surface we know that $Pic(X)\cong Num(X)\cong NS(X)$. A class $L\in Num(X)$ is called movable if $L.C\geq 0$ for every curve $C$ in $X$. It just means that $L$ is a movable class if it is nef.

The interior of this cone is the ample cone, by Nakai's criterion. So we could have big and nef bundles which are not ample isn't it?

Also can we have globally generated, big and nef line bundles on a K3 surface which are not ample? I suppose on the Kummer surface, we could find such examples, is that right?