Geodesic
A~Torelli theorem for algebraic surfaces of type~$K3$
Izvestiya. Mathematics , Tome 5 (1971) no. 3, pp. 547-588.

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In this paper it is proved that an algebraic surface of type $K3$ is uniquely determined by prescribing the integrals of its holomorphic differential forms with respect to a basis of cycles of the two-dimensional homology group, if the homology class of a hyperplane section is distinguished. 
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I. I. Pyatetskii-Shapiro; I. R. Shafarevich. A~Torelli theorem for algebraic surfaces of type~$K3$. Izvestiya. Mathematics , Tome 5 (1971) no. 3, pp. 547-588. http://geodesic.mathdoc.fr/item/IM2_1971_5_3_a4/

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