Nef line bundles on Calabi-Yau threefolds, I

We prove that a nef line bundle $\mathcal{L}$ with $c_1(\mathcal{L}{)}^2\mathrm{\ne }0$ on a Calabi-Yau threefold $X$ with Picard number $2$ and with $c_3(X)\mathrm{\ne }0$ is semiample, that is, some multiple of $\mathcal{L}$ is generated by global sections.