Kuga-Satake construction on families of K3 surfaces of Picard rank 14

Abstract

The isometry between the type IV$_6$ and the type II$_4$ hermitian symmetric domains suggests a possible relation between suitable moduli spaces of K3 surfaces of Picard rank $14$ and of polarised 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 the modular mapping can be realised for any specific families of K3 surfaces of Picard rank $14$, which can be specialised to families of K3 surfaces of higher Picard rank.