Threefolds with nef anticanonical bundles

We prove that the Albanese map of a smooth projective threefold, whose anticanonical bundle is nef, is a surjective submersion. We also investigate morphisms of threefolds to curves and surfaces whose relative anticanonical bundle are nef.Comment: plainTex, 47 pages, change in the introduction, paper will be appear in Collectanea mathematica 49, volume in honour of F.Serran

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

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