Prym varieties of genus four curves

Bruin, Nils; Sertöz, Emre

doi:10.1090/tran/7902

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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