Vol. 3, No. 4, 2018

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Droites sur les hypersurfaces cubiques

Jean-Louis Colliot-Thélène

Vol. 3 (2018), No. 4, 723–728
Abstract

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.

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 had already been given several other proofs.

Keywords
Chow groups, one-cycles, cubic hypersurfaces
Mathematical Subject Classification 2010
Primary: 14C15, 14C25, 14C35
Milestones
Received: 10 April 2018
Revised: 13 June 2018
Accepted: 4 July 2018
Published: 18 December 2018
Authors
Jean-Louis Colliot-Thélène
Laboratoire de Mathématiques d’Orsay
Université Paris-Sud, CNRS, Université Paris-Saclay
91405 Orsay
France