The movable cone of certain Calabi-Yau threefolds of Picard number two

TL;DR

This paper explicitly describes the chamber structure of the movable cone for certain Calabi-Yau threefolds with Picard number two, verifying the Morrison-Kawamata cone conjecture and classifying all birational minimal models.

Contribution

It provides an explicit description of the movable cone's chamber structure and verifies the Morrison-Kawamata cone conjecture for these Calabi-Yau threefolds, also classifying their minimal models.

Findings

Verified the Morrison-Kawamata cone conjecture for these threefolds.

Explicitly described the chamber structure of the movable cone.

Found all birational minimal models, finite up to isomorphism.

Abstract

We describe explicitly the chamber structure of the movable cone for a general smooth complete intersection Calabi-Yau threefold $X$ of Picard number two in certain Pr-ruled Fano manifold and hence verify the Morrison-Kawamata cone conjecture for such $X$. Moreover, all birational minimal models of such Calabi-Yau threefolds are found, whose number is finite up to isomorphism.