On isogenies among certain abelian surfaces

Abstract

We construct a three-parameter family of non-hyperelliptic and bielliptic plane genus-three curves whose associated Prym variety is two-isogenous to the Jacobian variety of a general hyperelliptic genus-two curve. Our construction is based on the existence of special elliptic fibrations with the section on the associated Kummer surfaces that provide a simple geometric interpretation for the rational double cover induced by the two-isogeny between the abelian surfaces.

33 pages; minor typos corrected in version 2

References in corpus (5)

• The Satake sextic in elliptic fibrations on K3
• A Universal Genus-Two Curve from Siegel Modular Forms
• Normal forms for Kummer surfaces
• Nikulin involutions and the CHL string
• On the geometry of (1,2)-polarized Kummer surfaces

Cited by in corpus (3)

• On K3 surfaces of Picard rank 14
• On the mixed-twist construction and monodromy of associated Picard-Fuchs systems
• On the duality of F-theory and the CHL string in seven dimensions