COSKUN, I. and PRENDERGAST-SMITH, A., 2017. Fano manifolds of index n-2 and the cone conjecture. Mathematical Proceedings of the Cambridge Philosophical Society, in press.
The Morrison–Kawamata Cone Conjecture predicts that the action of the automorphism
group on the effective nef cone and the action of the pseudo-automorphism group
on the effective movable cone of a klt Calabi-Yau pair have rational, polyhedral fundamental
domains. In [CPS], we proved the conjecture for certain blowups of Fano
manifolds of index n − 1. In this paper, we consider the Morrison–Kawamata conjecture
for blowups of Fano manifolds of index n − 2.