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Regular version of the site

Article

Moduli spaces of irreducible symplectic manifolds

Compositio Mathematica. 2010. Vol. 146. No. 2. P. 404-434.
Gritsenko V., Hulek K., Sankaran G.

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.

To resolve some geometric problems  we give a new, clear, formulation of Siegel's formula for the  number of representationс natural numbers by positive definite quadratic forms of  odd rank. It may be expressed either in terms of Zagier L-functions or in terms of the H.~Cohen numbers.