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

Adrian Clingher, Andreas Malmendier, Tanush Shaska

I-AIMS paper 2021-1 · Published in Pure Appl. Math. Q. 17 (2021), no. 5, 1739–1784 · 2021

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.

MSC classes: 14H40, 14J28

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