Description
The Kawamata-Morrison cone conjecture predicts that the
nef cone Nef(X) of a K-trivial projective manifold X is rational polyhedral, i.e. finitely
generated, up to the action of the automorphism group Aut(X). The conjecture was
proven in dimension 2, while in higher dimension just for abelian varieties,
holomorphic irreducible symplectic manifolds (IHS) and Enriques manifolds (étale
quotient of IHS). After giving a general overview on this problem, I present my
result concerning the validity of the cone conjecture for étale quotient of abelian
varieties, i.e. for Generalized Hyperelliptic Manifolds.
