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On the Griffiths group of the cubic sevenfold

Alberto Albano·Alberto Collino
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Abstract

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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Alberto Albano, Alberto Collino. 1993-08-03. On the Griffiths group of the cubic sevenfold. https://arxiv.org/abs/alg-geom/9308001

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