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Faculty Selected Works of Adrian Clingher
Article
Geometry of Prym Varieties for Special Bielliptic Curves of Genus Three and Five
Pure and Applied Mathematics Quarterly (2021)
  • Adrian Clingher, University of Missouri-St. Louis
  • Andreas Malmendier, Utah State University
  • Tony Shaska, Oakland University
Link
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
Disciplines
Publication Date
2021
DOI
10.4310/PAMQ.2021.v17.n5.a5
Citation Information
Adrian Clingher, Andreas Malmendier and Tony Shaska. "Geometry of Prym Varieties for Special Bielliptic Curves of Genus Three and Five" Pure and Applied Mathematics Quarterly Vol. 17 Iss. 5 (2021)
Available at: http://works.bepress.com/adrian-clingher/23/