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2021 On Isogenies Among Certain Abelian Surfaces
Adrian Clingher, Andreas Malmendier, Tony Shaska
Michigan Math. J. Advance Publication 1-43 (2021). DOI: 10.1307/mmj/20195790

Abstract

We construct a three-parameter family of nonhyperelliptic and bielliptic plane genus-three curves whose associated Prym variety is two-isogenous to the Jacobian variety of a general hyperelliptic genus-two curve. Our construction is based on the existence of special elliptic fibrations with the section on the associated Kummer surfaces that provide a simple geometric interpretation for the rational double cover induced by the two-isogeny between the Abelian surfaces.

Citation

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Adrian Clingher. Andreas Malmendier. Tony Shaska. "On Isogenies Among Certain Abelian Surfaces." Michigan Math. J. Advance Publication 1 - 43, 2021. https://doi.org/10.1307/mmj/20195790

Information

Received: 29 August 2019; Revised: 22 June 2020; Published: 2021
First available in Project Euclid: 23 December 2020

Digital Object Identifier: 10.1307/mmj/20195790

Subjects:
Primary: 14H40, 14J28

Rights: Copyright © 2021 The University of Michigan

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