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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Prym varieties of genus four curves
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by Nils Bruin and Emre Can Sertöz PDF
Trans. Amer. Math. Soc. 373 (2020), 149-183 Request permission


Double covers of a generic genus four curve C are in bijection with Cayley cubics containing the canonical model of C. The Prym variety associated to a double cover is a quadratic twist of the Jacobian of a genus three curve X. The curve X can be obtained by intersecting the dual of the corresponding Cayley cubic with the dual of the quadric containing C. We take this construction to its limit, studying all smooth degenerations and proving that the construction, with appropriate modifications, extends to the complement of a specific divisor in moduli. We work over an arbitrary field of characteristic different from two in order to facilitate arithmetic applications.
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Additional Information
  • Nils Bruin
  • Affiliation: Simon Fraser University, 8888 University Drive, Burnaby, British Columbia, V5A 1S6, Canada
  • MR Author ID: 653028
  • Email:
  • Emre Can Sertöz
  • Affiliation: Max Planck Institute for Mathematics in the Sciences, Inselstraße 22, 04103 Leipzig, Germany
  • Email:
  • Received by editor(s): September 4, 2018
  • Received by editor(s) in revised form: April 15, 2019
  • Published electronically: September 23, 2019
  • Additional Notes: Research of the first author partially supported by NSERC
  • © Copyright 2019 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 373 (2020), 149-183
  • MSC (2010): Primary 14H45, 14H40, 14H50
  • DOI:
  • MathSciNet review: 4042871