A simple criterion for the uniruledness of an orthogonal modular variety

Abstract

We exhibit a simple uniruledness criterion for general orthogonal modular varieties in terms of invariants of the corresponding lattice. As an application, we obtain the uniruledness of almost all Nikulin--Vinberg moduli spaces parameterizing projective K3 surfaces of Picard number at least 3 and fixed finite automorphism group.

15 pages, to appear in the volume 'Moduli Spaces and Modular Forms'