## 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

## 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.## References

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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: nbruin@sfu.ca
**Emre Can Sertöz**- Affiliation: Max Planck Institute for Mathematics in the Sciences, Inselstraße 22, 04103 Leipzig, Germany
- Email: emresertoz@gmail.com
- 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: https://doi.org/10.1090/tran/7902
- MathSciNet review: 4042871