On the relative Morrison-Kawamata cone conjecture

Abstract

We relate the Morrison-Kawamata cone conjecture for Calabi-Yau fiber spaces to the existence of Shokurov polytopes. For K3 fibrations, the existence of (weak) fundamental domains for movable cones is established. The relationship between the relative cone conjecture and the cone conjecture for its geometric or generic fibers is studied.

arXiv commentpublished version (which includes a correction to the proof of Theorem 2.5, Step 2)