Fano manifolds of index n-1 and the cone conjecture

The Morrison-Kawamata cone conjecture predicts that the actions of the automorphism group on the effective nef cone and the pseudo-automorphism group on the effective movable cone of a klt Calabi-Yau pair (X,Δ) have finite, rational polyhedral fundamental domains. Let Z be an n-dimensional Fano manifold of index n-1 such that -KZ=(n-1)H for an ample divisor H. Let Γ be the base locus of a general (n-1)-dimensional linear system V ⊂/H/. In this paper, we verify the Morrison-Kawamata cone conjecture for the blowup of Z along Γ. © 2013 The Author(s). Published by Oxford University Press. All rights reserved.