Hyperelliptic genus 4 curves on abelian surfaces
  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. 
Pawe{\l} Bor\'owka, G. K. Sankaran
math.AG