On the Numerical Dimension of Calabi–Yau 3-Folds of Picard Number 2

Abstract

Abstract We show that for any smooth Calabi–Yau threefold $X$ of Picard number $2$ with infinite birational automorphism group, the numerical dimension $\kappa _\sigma $ of the extremal rays of the movable cone of $X$ is $\frac {3}{2}$. Furthermore, we provide new examples of Calabi–Yau threefolds of Picard number $2$ with infinite birational automorphism group.