Seminar

In many cases moduli spaces can be written as the quotient of a homogeneous domain by an arithmetic group. Prime examples are moduli spaces of abelian varieties or K3 surfaces. This representation can be used to derive geometric properties of these moduli spaces such as the Kodaria dimension. In the case of irreducible symplectic manifolds one can, in spite of the lack of the global Torelli theorem, still use this technique to prove general type results. Other applications include results on the fundamental group of moduli spaces. We shall give an introduction to the topic focussing on general ideas rather than technical details.