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Prym varieties of double coverings of elliptic curves

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We prove the generic injectivity of the Prym map $\mathscr{P}: \mathcal{R}_{1, r} \rightarrow \mathcal{A}_{\frac{r}{2}}^\delta$ sending a double covering of an elliptic curve ramified at $r \geq 6$ points to its polarized Prym variety. For $r=6$ the map is birational and both $\mathcal{R}_{1,6}$ and $\mathcal{A}_3^\delta$ are unirational.

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International Mathematics Research Notices, 2014, vol. 2014, num. 6, p. 1689-1698

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(c) Marcucci, Valeria Ornella et al., 2014

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Articles publicats en revistes (Matemàtiques i Informàtica)

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Prym varieties of double coverings of elliptic curves