We study the moduli spaces of polarised irreducible symplectic manifolds. By a comparison with locally symmetric varieties of orthogonal type of dimension 20, we show that the moduli space of polarised deformation K3() manifolds with polarisation of degree 2d and split type is of general type if d >= 12.
- orthogonal groups
- irreducible symplectic manifold
- Siegel formula for quadratic forms