Emma Brakkee : General type results for moduli of hyperkähler varieties

In 2007, Gritsenko, Hulek and Sankaran proved that the moduli space of
K3 surfaces of degree 2d is of general type when d>61. Their strategy is
to reduce the question to the existence of a certain cusp form for an
orthogonal modular variety. This method has been applied successfully to
prove general type results for, among others, some moduli of
higher-dimensional hyperkähler varieties.
In this talk, we sketch the reduction argument and give general type
results for some more types of hyperkähler moduli spaces. We also
explain what the challenges are when trying to imitate the strategy for
other moduli spaces of hyperkähler varieties. This is joint work in
progress with I. Barros, P. Beri and L. Flapan.