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arXiv · 2005.04839

Geometry of Prym varieties for special bielliptic curves of genus three and five

Adrian Clingher·Andreas Malmendier·Tony Shaska
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Abstract

We construct two pencils of bielliptic curves of genus three and genus five. The first pencil is associated with a general abelian surface with a polarization of type $(1,2)$. The second pencil is related to the first by an unramified double cover, the Prym variety of which is canonically isomorphic to the Jacobian of a very general curve of genus two. Our results are obtained by analyzing suitable elliptic fibrations on the associated Kummer surfaces and rational double covers among them.

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Adrian Clingher, Andreas Malmendier, Tony Shaska. 2020-05-11. Geometry of Prym varieties for special bielliptic curves of genus three and five. https://doi.org/10.4310/pamq.2021.v17.n5.a5

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