On the geometry of (1,2)-polarized Kummer surfaces

Abstract

We discuss several geometric features of a Kummer surface associated with a (1,2)-polarized abelian surface defined over the field of complex numbers. In particular, we show that any such Kummer surface can be modeled as the double cover of the projective plane branched along six lines, three of which meet a common point. The proof uses certain explicit pencils of plane quartic bielliptic genus-three curves whose associated Prym varieties are naturally (1,2)-polarized abelian surfaces.