Izvestiya. Mathematics, Tome 4 (1970) no. 3, pp. 520-526
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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/
@article{IM2_1970_4_3_a2,
author = {A. M. Shermenev},
title = {On the motif of a cubic hypersurface},
journal = {Izvestiya. Mathematics},
pages = {520--526},
year = {1970},
volume = {4},
number = {3},
language = {en},
url = {http://geodesic.mathdoc.fr/item/IM2_1970_4_3_a2/}
}
TY - JOUR
AU - A. M. Shermenev
TI - On the motif of a cubic hypersurface
JO - Izvestiya. Mathematics
PY - 1970
SP - 520
EP - 526
VL - 4
IS - 3
UR - http://geodesic.mathdoc.fr/item/IM2_1970_4_3_a2/
LA - en
ID - IM2_1970_4_3_a2
ER -
%0 Journal Article
%A A. M. Shermenev
%T On the motif of a cubic hypersurface
%J Izvestiya. Mathematics
%D 1970
%P 520-526
%V 4
%N 3
%U http://geodesic.mathdoc.fr/item/IM2_1970_4_3_a2/
%G en
%F IM2_1970_4_3_a2
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.
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[3] Gherardelli F., “Un osservazione sulla varieta'cubica di $\mathbf P^4$”, Rend. Sem. Mat. Fis. Milano, 37 (1967), 157–160 | DOI | MR | Zbl
