Nef Line Bundles on Calabi–Yau Threefolds, I

Abstract

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