Hyperelliptic genus 4 curves on abelian surfaces
Algebraic Geometry
2019-11-13 v1
Abstract
We study smooth curves on abelian surfaces, especially for genus 4, when the complementary subvariety in the Jacobian is also a surface. We show that up to translation there is exactly one genus 4 hyperelliptic curve on a general (1, 3)-polarised abelian surface. We investigate these curves and show that their Jacobians contain a surface and its dual as complementary abelian subvarieties.
Cite
@article{arxiv.1606.09301,
title = {Hyperelliptic genus 4 curves on abelian surfaces},
author = {Paweł Borówka and G. K. Sankaran},
journal= {arXiv preprint arXiv:1606.09301},
year = {2019}
}