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 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.

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

References in corpus (1)

• The Kodaira dimension of the moduli of K3 surfaces

Cited by in corpus (32)

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• Induced Automorphisms on Irreducible Symplectic Manifolds
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• Moduli of double EPW-sextics
• Tautological classes on moduli space of hyperkähler manifolds
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• Powers of Jacobi triple product, Cohen's numbers and the Ramanujan $\Delta$-function
• On the nonsymplectic involutions of the Hilbert square of a K3 surface
• Mukai models and Borcherds products
• On the Kodaira Dimension of the Moduli of Deformation Generalised Kummer Varieties
• On the image of the period map for polarized hyperkähler manifolds
• Any component of moduli of polarized hyperkaehler manifolds is dense in its deformation space
• Fano varieties of cubic fourfolds containing a plane
• Intersection numbers of extremal rays on holomorphic symplectic varieties
• Non-symplectic automorphisms of odd prime order on manifolds of $K{3}^{[n]}$-type
• Irregular cusps of orthogonal modular varieties
• MBM classes and contraction loci on low-dimensional hyperkahler manifolds of K3 type
• Galois representations on the cohomology of hyper-Kähler varieties
• On birational transformations of Hilbert schemes of points on K3 surfaces
• Periods of Double EPW-sextics
• Kodaira dimension of universal holomorphic symplectic varieties
• Boundary combinatorics of orthogonal modular 4-folds
• The Moser isotopy for holomorphic symplectic and C-symplectic structures
• A special Debarre-Voisin fourfold