Hyperelliptic genus 4 curves on abelian surfaces

Borówka, Paweł; Sankaran, G.

doi:10.1090/proc/13795

Hyperelliptic genus 4 curves on abelian surfaces
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by Paweł Borówka and G. K. Sankaran PDF

Proc. Amer. Math. Soc. 145 (2017), 5023-5034 Request permission

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.

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