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Transactions of the American Mathematical Society

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

 
 

 

Prym varieties of genus four curves


Authors: Nils Bruin and Emre Can Sertöz
Journal: Trans. Amer. Math. Soc. 373 (2020), 149-183
MSC (2010): Primary 14H45, 14H40, 14H50
DOI: https://doi.org/10.1090/tran/7902
Published electronically: September 23, 2019
MathSciNet review: 4042871
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Abstract: 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
Email: nbruin@sfu.ca

Emre Can Sertöz
Affiliation: Max Planck Institute for Mathematics in the Sciences, Inselstraße 22, 04103 Leipzig, Germany
Email: emresertoz@gmail.com

DOI: https://doi.org/10.1090/tran/7902
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
Article copyright: © Copyright 2019 American Mathematical Society