On Isogenies Among Certain Abelian Surfaces

Adrian Clingher; Andreas Malmendier; Tony Shaska

doi:10.1307/MMJ/20195790

On Isogenies Among Certain Abelian Surfaces

Adrian Clingher, Andreas Malmendier, Tony Shaska

University of Missouri-St. Louis

Research output: Contribution to journal › Article › peer-review

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.

Original language	American English
Journal	The Michigan Mathematical Journal
Volume	71
DOIs	https://doi.org/10.1307/MMJ/20195790
State	Published - 2022

Disciplines

Physical Sciences and Mathematics

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title = "On Isogenies Among Certain Abelian Surfaces",

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. ",

author = "Adrian Clingher and Andreas Malmendier and Tony Shaska",

note = "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.",

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AU - Clingher, Adrian

AU - Malmendier, Andreas

AU - Shaska, Tony

N1 - 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.

PY - 2022

Y1 - 2022

N2 - 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.

AB - 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.

UR - https://doi.org/10.1307/mmj/20195790

U2 - 10.1307/MMJ/20195790

DO - 10.1307/MMJ/20195790

M3 - Article

VL - 71

JO - The Michigan Mathematical Journal

JF - The Michigan Mathematical Journal

ER -

On Isogenies Among Certain Abelian Surfaces

Abstract

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