Geodesic
An analogue of the Torelli theorem for Kummer surfaces of Jacobians
Izvestiya. Mathematics , Tome 8 (1974) no. 1, pp. 21-41

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In this paper we obtain algebraic criteria that isolate the class of Kummer surfaces of Jacobians of curves of genus 2 within the class of $K3$ surfaces. In addition, we prove analogues of Torelli's theorems for these surfaces and find a “standard” representation for them as a complete intersection of three quadrics in $\mathbf P^5$. 
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     author = {V. V. Nikulin},
     title = {An analogue of the {Torelli} theorem for {Kummer} surfaces of {Jacobians}},
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V. V. Nikulin. An analogue of the Torelli theorem for Kummer surfaces of Jacobians. Izvestiya. Mathematics , Tome 8 (1974) no. 1, pp. 21-41. http://geodesic.mathdoc.fr/item/IM2_1974_8_1_a2/