Abstract:
Let M be a holomorphically symplectic manifold, and K be its Kaehler cone. We show that all faces of the Kahler cone of M are hyperplanes orthogonal to certain homology classes, called MBM classes. The MBM classes can be characterized as homology classes which can be represented by a minimal curve in some deformation of M. For a deformation of a Hilbert scheme on K3, this result gives a simple proof of the Morrison-Kawamata cone conjecture (proven by Markman and Yoshioka in a forthcoming paper). This is a joint work with Ekaterina Amerik.