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Izv. Akad. Nauk SSSR Ser. Mat., 1970, Volume 34, Issue 3, Pages 515–522 (Mi izv2432)  

This article is cited in 1 scientific paper (total in 1 paper)

On the motif of a cubic hypersurface

A. M. Shermenev


Abstract: 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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English version:
Mathematics of the USSR-Izvestiya, 1970, 4:3, 520–526

Bibliographic databases:

UDC: 513.6
MSC: 14Q10, 14J70, 14J50, 14Q15
Received: 11.06.1969

Citation: A. M. Shermenev, “On the motif of a cubic hypersurface”, Izv. Akad. Nauk SSSR Ser. Mat., 34:3 (1970), 515–522; Math. USSR-Izv., 4:3 (1970), 520–526

Citation in format AMSBIB
\Bibitem{She70}
\by A.~M.~Shermenev
\paper On the motif of a cubic hypersurface
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1970
\vol 34
\issue 3
\pages 515--522
\mathnet{http://mi.mathnet.ru/izv2432}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=262245}
\zmath{https://zbmath.org/?q=an:0213.22703}
\transl
\jour Math. USSR-Izv.
\yr 1970
\vol 4
\issue 3
\pages 520--526
\crossref{https://doi.org/10.1070/IM1970v004n03ABEH000918}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Yu. I. Manin, M. A. Tsfasman, “Rational varieties: algebra, geometry and arithmetic”, Russian Math. Surveys, 41:2 (1986), 51–116  mathnet  crossref  mathscinet  zmath  adsnasa  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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