On the numerical dimension of Calabi-Yau 3-folds of Picard number 2

TL;DR

This paper investigates the numerical dimension of extremal rays in the movable cone of certain Calabi-Yau threefolds with Picard number 2, revealing it to be 3/2, and introduces new examples with infinite birational automorphism groups.

Contribution

It establishes the numerical dimension as 3/2 for these threefolds and provides new examples with infinite birational automorphism groups.

Findings

Numerical dimension of extremal rays is 3/2.

New examples of Calabi-Yau threefolds with infinite birational automorphism groups.

Enhanced understanding of the movable cone structure.

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.