Fano manifolds of index n-1 and the cone conjecture

Abstract

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 $(X,\Delta )$ have finite, rational polyhedral fundamental domains. Let $Z$ be an $n$-dimensional Fano manifold of index $n-1$ such that $-K_Z=(n-1)H$ for an ample divisor $H$. Let $\Gamma$ be the base locus of a general $(n-1)$-dimensional linear system $V\subset |H|$. In this paper, we verify the Morrison-Kawamata cone conjecture for the blow-up of $Z$ along $\Gamma$.

30 pages

References in corpus (1)

• The cone conjecture for abelian varieties