Prym varieties of genus four curves
Nils Bruin and Emre Sertöz
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Submission date: 27. Aug. 2018
published in: Transactions of the American Mathematical Society, 373 (2020) 1, p. 149-183
DOI number (of the published article): 10.1090/tran/7902
MSC-Numbers: 14H45, 14H40, 14H50
Keywords and phrases: algebraic curves, projective geometry, Prym varieties
Link to arXiv: See the arXiv entry of this preprint.
Double covers of a generic genus four curve C are in bijection with Cayley cubics containing the canonical model of C. The dual of one such cubic intersected with the dual of the quadric containing C yields the genus three Prym curve corresponding to the double cover. 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.