Title: The Morrison Cone Conjecture under deformation
Abstract: Let Y be a Calabi-Yau manifold. The Morrison Cone Conjecture is a fundamental conjecture in Algebraic Geometry on the geometry of the nef cone Nef(Y) and the movable cone Mov(Y): while these cones are in general not rational polyhedral, the cone conjecture predicts that the action of Aut(Y) on Nef(Y) admits a rational polyhedral fundamental domain, and that the action of Bir(Y) on Mov(Y) admits a rational polyhedral fundamental domain. Even though the conjecture has been settled in special cases, it is still wide open in dimension at least 3. We prove that if the cone conjecture holds for a smooth Calabi-Yau threefold Y, then it also holds for any smooth deformation of Y.