On the Griffiths group of the cubic sevenfold

Details On the Griffiths group of the cubic sevenfold On the Griffiths group of the cubic sevenfold

1993-08-03

arxiv.org/abs/alg-geom/9308001v1

Mathematics

Algebraic Geometry

12 pages, AmSTeX 2.1

Scientific paper

We prove that the Griffiths group of 3-cycles homologous to zero modulo algebraic equivalence, on a generic hypersurfaces of dimension 7 and degree 3 is not finitely generated, even when tensored with Q. Using this and a result of Nori, we give examples of varieties for which some Griffiths group is not finitely generated (modulo torsion) but whose corresponding intermediate Jacobian is trivial.

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