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Moduli spaces of irreducible symplectic manifolds

Part of: Surfaces and higher-dimensional varieties Compact analytic spaces Forms and linear algebraic groups Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  26 January 2010

V. Gritsenko ,
K. Hulek  and
G. K. Sankaran
V. Gritsenko
Affiliation:
Université Lille 1, Laboratoire Paul Painlevé, F-59655 Villeneuve d’Ascq, Cedex, France (email: valery.gritsenko@math.univ-lille1.fr)
K. Hulek
Affiliation:
Institut für Algebraische Geometrie, Leibniz Universität Hannover, D-30060 Hannover, Germany (email: hulek@math.uni-hannover.de)
G. K. Sankaran
Affiliation:
Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK (email: gks@maths.bath.ac.uk)
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Abstract

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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[2] manifolds with polarisation of degree 2d and split type is of general type if d≥12.

Keywords

irreducible symplectic manifoldmoduliorthogonal groupsSiegel formula for quadratic forms.

MSC classification

Secondary: 14J15: Moduli, classification 11E25: Sums of squares and representations by other particular quadratic forms 11F55: Other groups and their modular and automorphic forms (several variables) 14J35: $4$-folds 32J27: Compact Kähler manifolds
Type
Research Article
Information
Compositio Mathematica , Volume 146 , Issue 2 , March 2010 , pp. 404 - 434
Copyright
Copyright © Foundation Compositio Mathematica 2010

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