Emma Brakkee : General type results for moduli of hyperkähler varietiesSéminaire « Géométrie algébrique »
Salle Kampé de Feriet (Bâtiment M2, 1er étage)
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.