English

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.

Keywords

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}
}
R2 v1 2026-06-22T14:39:05.447Z