Kodaira dimensions of some moduli spaces of hyperkähler fourfolds

Abstract: We use modular forms to study the birational geometry of some moduli spaces of hyperkähler fourfolds. I'll review a bit of the algebraic geometry of these moduli spaces, and then I'll explain some methods, due to Gritsenko, Hulek, and Sankaran, for computing their Kodaira dimensions. These methods make use of special modular forms defined on high rank orthogonal groups. I'll also report on an ongoing project with Jen Berg applying related techniques to certain moduli spaces of Enriques surfaces.

algebraic geometry

Audience: researchers in the topic

UBC Vancouver Algebraic Geometry Seminar

Series comments: Recordings and slides are available on the seminar webpage:

wiki.math.ubc.ca/mathbook/alggeom-seminar/Main_Page