Hyperelliptic genus 4 curves on abelian surfaces

Paweł Borówka; G. K. Sankaran

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arXiv · 1606.09301

Hyperelliptic genus 4 curves on abelian surfaces

Paweł Borówka·G. K. Sankaran

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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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Paweł Borówka, G. K. Sankaran. 2016-06-29. Hyperelliptic genus 4 curves on abelian surfaces. https://arxiv.org/abs/1606.09301

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