Geodesic
On the motif of a cubic hypersurface
Izvestiya. Mathematics , Tome 4 (1970) no. 3, pp. 520-526

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We consider a nonsingular cubic hypersurface $V$ in $\mathbf P^4$. We prove that the motif $\widetilde V$ can be expressed by means of the Tate motif and the motif $(Y,\frac12\operatorname{id}-\frac12c(\gamma))$, where $Y$ is the curve of straight lines on $V$ that pass through a fixed line $l_0\subset V$ and $\gamma$ is an automorphism of $Y$ that leaves no line coplanar with $l_0$ fixed. 
@article{IM2_1970_4_3_a2,
     author = {A. M. Shermenev},
     title = {On the motif of a cubic hypersurface},
     journal = {Izvestiya. Mathematics },
     pages = {520--526},
     publisher = {mathdoc},
     volume = {4},
     number = {3},
     year = {1970},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1970_4_3_a2/}
}
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A. M. Shermenev. On the motif of a cubic hypersurface. Izvestiya. Mathematics , Tome 4 (1970) no. 3, pp. 520-526. http://geodesic.mathdoc.fr/item/IM2_1970_4_3_a2/