On K3 surfaces of Picard rank 14

Abstract

We study complex algebraic K3 surfaces with finite automorphism groups and polarized by rank 14, 2‐elementary lattices. Three such lattices exist, namely, , , and . As part of our study, we provide birational models for these surfaces as quartic projective hypersurfaces and describe the associated coarse moduli spaces in terms of suitable modular invariants. Additionally, we explore the connection between these families and dual K3 families related via the Nikulin construction.