Kuga–Satake Construction on Families of K3 Surfaces of Picard Rank 14

Abstract

The isometry between the type IV₆ and the type II₄ hermitian symmetric domains suggests a possible relation between suitable moduli spaces of K3 surfaces of Picard rank 14 and of polarized abelian 8-folds with totally definite quaternion multiplication. We show how this isometry induces a geometrically meaningful map between such moduli spaces using the Kuga–Satake construction. Furthermore, we illustrate how the modular mapping can be realized for some specific families of K3 surfaces of Picard rank 14, which can be specialized to families of K3 surfaces of higher Picard rank.