doi:10.1093/imrn/rnv071 Families of Lattice Polarized K3 Surfaces with Monodromy

We extend the notion of lattice polarization for K3 surfaces to families over a (not neces-sarily simply connected) base, in a way that gives control over the action of monodromy on the algebraic cycles, and discuss the uses of this new theory in the study of families of K3 surfaces admitting fibrewise symplectic automorphisms. We then give an applica-tion of these ideas to the study of Calabi-Yau three-folds admitting fibrations by lattice polarized K3 surfaces.