English

On isogenies among certain abelian surfaces

Algebraic Geometry 2022-05-26 v2

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.

Keywords

Cite

@article{arxiv.1901.09846,
  title  = {On isogenies among certain abelian surfaces},
  author = {Adrian Clingher and Andreas Malmendier and Tony Shaska},
  journal= {arXiv preprint arXiv:1901.09846},
  year   = {2022}
}

Comments

33 pages; minor typos corrected in version 2

R2 v1 2026-06-23T07:24:27.036Z