Elliptic K3 surfaces - monodromy strata versus lattice polarizations
Bogomolov, Petrov and Tschinkel defined monodromy strata in the moduli space of elliptic K3 surfaces (BPT strata) and they also proved that these strata are rational. Here we compare (some of) these BPT strata to moduli spaces of lattice polarized K3 surfaces. More precisely, we classify all moduli spaces of lattice polarized K3 surfaces which dominate finite to one one of the BPT strata. This is closely related to Shimada's classification of connected components of the moduli of elliptic K3 surfaces.
This is joint work with Michael Lönne.