Klaus Hulek, Leibniz Universität Hannover
Many moduli spaces can be realized as (open subsets of) ball quotients. This includes moduli of cubic surfaces, moduli of point configurations and various moduli spaces of K3 surfaces. Typically, these moduli spaces can be viewed both from a Hodge theory point of view as well as a GIT perspective. This leads to different natural compactifications which are often related in subtle ways. In this talk I want to discuss the birational geometry of some of these spaces.
This covers joint work with Casalaina-Martin, Grushevsky, Laza on the one hand and Maeda on the other hand.