Some properties of second order theta functions on Prym varieties

E. Izadi; C. Pauly

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Some properties of second order theta functions on Prym varieties

E. Izadi·C. Pauly

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Abstract

Let $P \cup P'$ be the two component Prym variety associated to an étale double cover $\tilde{C} \to C$ of a non-hyperelliptic curve of genus $g \geq 6$ and let $|2Ξ_0|$ and $|2Ξ_0'|$ be the linear systems of second order theta divisors on $P$ and $P'$ respectively. The component $P'$ contains canonically the Prym curve $\tilde{C}$. We show that the base locus of the subseries of divisors containing $\tilde{C} \subset P'$ is scheme-theoretically the curve $\tilde{C}$. We also prove canonical isomorphisms between some subseries of $|2Ξ_0|$ and $|2Ξ_0'|$ and some subseries of second order theta divisors on the Jacobian of $C$.

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E. Izadi, C. Pauly. 1999-09-09. Some properties of second order theta functions on Prym varieties. https://arxiv.org/abs/math/9904001

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