Geodesic
Cubic hypersurfaces. I. Quasigroups of classes of points
Izvestiya. Mathematics , Tome 2 (1968) no. 6, pp. 1171-1191.

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In this paper we introduce and study algebraic structures on the set of points of a cubic hypersurface that are associated with the composition of points by means of drawing of straight lines. 
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Yu. I. Manin. Cubic hypersurfaces. I. Quasigroups of classes of points. Izvestiya. Mathematics , Tome 2 (1968) no. 6, pp. 1171-1191. http://geodesic.mathdoc.fr/item/IM2_1968_2_6_a0/

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