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.
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