Intersection numbers of extremal rays on holomorphic symplectic varieties
arXiv:0909.4745
Abstract
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 collect evidence supporting our conjectures in specific cases.
24 pages; revision based on comments from the referees and results of Eyal Markman (arXiv:0912.4981)
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