2-cycles sur les hypersurfaces cubiques de dimension 5

Lie Fu; Zhiyu Tian

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arXiv · 1801.03995

2-cycles sur les hypersurfaces cubiques de dimension 5

Lie Fu·Zhiyu Tian

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Abstract

On \'etudie les cycles alg\'ebriques de codimension 3 sur les hypersurfaces cubiques lisses de dimension 5. Pour une telle hypersurface, on d\'emontre d'une part que son groupe de Griffiths des cycles de codimension 3 est trivial et d'autre part que l'application d'Abel-Jacobi induit un isomorphisme entre son groupe de Chow des cycles de codimension 3 alg\'ebriquement equivalents \`a z\'ero et sa jacobienne interm\'ediaire. ---------- We study 2-cycles of a smooth cubic hypersurface of dimension 5. We show that the Griffiths group of 2-cycles is trivial and the Abel-Jacobi map induces an isomorphism between the Chow group of algebraically trivial 2-cycles and the intermediate Jacobian.

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Lie Fu, Zhiyu Tian. 2018-01-11. 2-cycles sur les hypersurfaces cubiques de dimension 5. https://arxiv.org/abs/1801.03995

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