The Morrison Cone Conjecture under Deformation

Abstract

We prove that the Morrison--Kawamata cone conjecture is invariant under deformation for smooth Calabi--Yau threefolds. The proof compares the nef and movable cones of $Y$ to those of a very general deformation of $Y$ via Weyl groups naturally associated to $Y$. We use this result to prove new cases of the cone conjecture.

arXiv commentMajor improvements to exposition in Section 4-6. Main results unchanged