Moduli spaces of irreducible symplectic manifolds

Abstract

We study the moduli spaces of polarised irreducible symplectic manifolds. By a comparison with locally symmetric varieties of orthogonal type of dimension20, we show that the moduli space of polarised deformation K3 [2] manifolds with polarisation of degree 2d and split type is of general type if d≥12. © 2010 Foundation Compositio Mathematica.