A proof of the Kawamata-Morrison Cone Conjecture for holomorphic   symplectic varieties of K3^[n] or generalized Kummer deformation type
  We prove a version of the Kawamata-Morrison ample cone conjecture for projective irreducible holomorphic symplectic manifolds deformation equivalent to either the Hilbert scheme of n points on a K3 surface, or a generalized Kummer variety. 
Eyal Markman and Kota Yoshioka
math.AG