Algebraic Geometry Seminar: Brendan Hassett (Rice University)

We propose a general framework governing the intersection properties of extremal rays of irreducible holomorphic symplectic manifolds under the Beauville-Bogomolov form. Our main thesis is that extremal rays associated to Lagrangian projective subspaces control the behavior of the cone of curves. We explore implications of this philosophy for examples like Hilbert schemes of points on K3 surfaces and generalized Kummer varieties. We also present evidence supporting our conjectures in specific cases. (joint with Y. Tschinkel)