Geodesic
The global Torelli theorem for Prym varieties at a~generic point
Izvestiya. Mathematics , Tome 20 (1983) no. 2, pp. 235-257

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In this paper it is proved that any unramified double cover of a sufficiently general (in the sense of moduli) curve of genus $\geqslant9$ can be uniquely recovered from its Prym variety with its canonical polarization. Bibliography: 23 titles. 
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     author = {V. I. Kanev},
     title = {The global {Torelli} theorem for {Prym} varieties at a~generic point},
     journal = {Izvestiya. Mathematics },
     pages = {235--257},
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     volume = {20},
     number = {2},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1983_20_2_a2/}
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V. I. Kanev. The global Torelli theorem for Prym varieties at a~generic point. Izvestiya. Mathematics , Tome 20 (1983) no. 2, pp. 235-257. http://geodesic.mathdoc.fr/item/IM2_1983_20_2_a2/