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We prove a version of the Kawamata-Morrison ample cone conjecture forprojective irreducible holomorphic symplectic manifolds deformation equivalentto either the Hilbert scheme of n points on a K3 surface, or a generalizedKummer variety.

A proof of the Kawamata-Morrison Cone Conjecture for holomorphic symplectic varieties of K3^[n] or generalized Kummer deformation type