On the Cone conjecture for Calabi-Yau manifolds with Picard number two

Abstract

Following a recent work of Oguiso, we calculate explicitly the groups of automorphisms and birational automorphisms on a Calabi-Yau manifold with Picard number two. When the group of birational automorphisms is infinite, we prove that the Cone conjecture of Morrison and Kawamata holds.Comment: to appear in Math. Res. Let