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MiS Preprint

Prym varieties of genus four curves

Nils Bruin and Emre Sertöz


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.

MSC Codes:
14H45, 14H40, 14H50
algebraic curves, projective geometry, Prym varieties

Related publications

2020 Repository Open Access
Nils Bruin and Emre Can Sertöz

Prym varieties of genus four curves

In: Transactions of the American Mathematical Society, 373 (2020) 1, pp. 149-183