Nils Bruin
Arithmetic properties of some low-level quartic modular threefolds
Two Siegel modular threefolds of low level allow for quartic birational models in projective space: A2(2) is birational to the Igusa (also called Castelnuovo-Richmond) quartic and A2(3) is birational to the Burkhardt quartic.
These models have some beautiful geometric properties that have been studied extensively. Their arithmetic is equally interesting. For instance, for the Burkhardt quartic one can ask which of its twists are rational or unirational, and also what the moduli interpretation they admit. For Igusa quartics there are interesting questions concerning their moduli interpretations as well. We will give an overview of the various results one can obtain.
This talk is based on joint works with Brett Nasserden, Eugene Filatov, and Avinash Kulkarni.