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arXiv · 1703.09644

Droites sur les hypersurfaces cubiques

Jean-Louis Colliot-Thélène
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Abstract

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 engendré par les droites. Le cas lisse est un théorème connu. La démonstration ici donnée repose sur un résultat sur les surfaces géométriquement rationnelles sur un corps quelconque (1983), obtenu via la K-théorie algébrique.

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Jean-Louis Colliot-Thélène. 2017-03-28. Droites sur les hypersurfaces cubiques. https://doi.org/10.2140/akt.2018.3.723

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