Geometry of Prym Varieties for Special Bielliptic Curves of Genus Three and Five

Adrian Clingher; Andreas Malmendier; Tony Shaska

doi:10.4310/PAMQ.2021.v17.n5.a5

Geometry of Prym Varieties for Special Bielliptic Curves of Genus Three and Five

Adrian Clingher, Andreas Malmendier, Tony Shaska

University of Missouri-St. Louis

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

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) (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.

Original language	American English
Journal	Pure and Applied Mathematics Quarterly
Volume	17
DOIs	https://doi.org/10.4310/PAMQ.2021.v17.n5.a5
State	Published - 2021

Keywords

Kummer surfaces
Prym varieties
isogenies of abelian surfaces

Disciplines

Physical Sciences and Mathematics

Access to Document

10.4310/PAMQ.2021.v17.n5.a5License: Unspecified

Cite this

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title = "Geometry of Prym Varieties for Special Bielliptic Curves of Genus Three and Five",

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) (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. ",

keywords = "Kummer surfaces, Prym varieties, isogenies of abelian surfaces",

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

note = "Pages: 1739 - 1784 DOI: https://dx.doi.org/10.4310/PAMQ.2021.v17.n5.a5 Authors Adrian Clingher (Department of Mathematics and Statistics, University of Missouri, St. Louis, Mo., U.S.A.) Andreas Malmendier (Department of Mathematics, University of Connecticut, Storrs, Ct., U.S.A.; and Department of Mathematics and Statistics, Utah State University, Logan, Ut., U.S.A.) Tony Shaska (Department of Mathematics and Statistics, Oakland University, Rochester, Michigan, U.S.A.)",

year = "2021",

doi = "10.4310/PAMQ.2021.v17.n5.a5",

language = "American English",

volume = "17",

journal = "Pure and Applied Mathematics Quarterly",

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TY - JOUR

T1 - Geometry of Prym Varieties for Special Bielliptic Curves of Genus Three and Five

AU - Clingher, Adrian

AU - Malmendier, Andreas

AU - Shaska, Tony

N1 - Pages: 1739 - 1784 DOI: https://dx.doi.org/10.4310/PAMQ.2021.v17.n5.a5 Authors Adrian Clingher (Department of Mathematics and Statistics, University of Missouri, St. Louis, Mo., U.S.A.) Andreas Malmendier (Department of Mathematics, University of Connecticut, Storrs, Ct., U.S.A.; and Department of Mathematics and Statistics, Utah State University, Logan, Ut., U.S.A.) Tony Shaska (Department of Mathematics and Statistics, Oakland University, Rochester, Michigan, U.S.A.)

PY - 2021

Y1 - 2021

N2 - 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) (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.

AB - 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) (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.

KW - Kummer surfaces

KW - Prym varieties

KW - isogenies of abelian surfaces

UR - https://dx.doi.org/10.4310/PAMQ.2021.v17.n5.a5

U2 - 10.4310/PAMQ.2021.v17.n5.a5

DO - 10.4310/PAMQ.2021.v17.n5.a5

M3 - Article

VL - 17

JO - Pure and Applied Mathematics Quarterly

JF - Pure and Applied Mathematics Quarterly

ER -

Geometry of Prym Varieties for Special Bielliptic Curves of Genus Three and Five

Abstract

Keywords

Disciplines

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