Moduli spaces of irreducible symplectic manifolds

Mathematics – Algebraic Geometry

Scientific paper

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Exposition improved, Reference to work of Debarre and Voisin added, Corollary 1.6 removed

Scientific paper

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 2d polarised (split type) symplectic
manifolds which are deformation equivalent to degree 2 Hilbert schemes of a K3
surface is of general type if d is at least 12.

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