On Numerical Dimensions of Calabi–Yau Varieties.

Let |$X$| be a Calabi–Yau variety of Picard number two with infinite birational automorphism group. We show that the numerical dimension |$\kappa ^{\mathbb{R}}_{\sigma }$| of the extremal rays of the closed movable cone of |$X$| is |$\dim X/2$|⁠. More generally, we investigate the relation between the two numerical dimensions |$\kappa ^{\mathbb{R}}_{\sigma }$| and |$\kappa ^{\mathbb{R}}_{\textrm{vol}}$| for Calabi–Yau varieties. We also compute |$\kappa ^{\mathbb{R}}_{\sigma }$| for non-big divisors in the closed movable cone of a projective hyperkähler manifold. [ABSTRACT FROM AUTHOR]