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arxiv: 1703.09644 · v1 · pith:FXIJORXKnew · submitted 2017-03-28 · 🧮 math.AG

Droites sur les hypersurfaces cubiques

classification 🧮 math.AG
keywords dimensionhypersurfacechowcyclesdroitesalreadybeencase
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Over any complex cubic hypersurface of dimension at least 2, the Chow group of 1-dimensional cycles is spanned by the lines lying on the hypersurface. The smooth case has already been given several other proofs. -- On montre que sur toute hypersurface cubique complexe de dimension au moins 2, le groupe de Chow des cycles de dimension 1 est engendr\'e par les droites. Le cas lisse est un th\'eor\`eme connu. La d\'emonstration ici donn\'ee repose sur un r\'esultat sur les surfaces g\'eom\'etriquement rationnelles sur un corps quelconque (1983), obtenu via la K-th\'eorie alg\'ebrique.

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