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Algebraic cycles on certain Calabi-Yau threefolds. (English) Zbl 0791.14017
The authors propose a method to study the Griffiths group of codimension two cycles on Calabi-Yau 3-folds \(X\) that are complete intersections in some ambient variety \(Y\). Surfaces in the Noether-Lefschetz locus of codimension two cycles on \(Y\) are used to produce interesting cycles on \(X\) by intersection. The Abel-Jacobi invariants of these cycles are studied by an infinitesimal method. In particular it is shown that under certain assumptions on the geometry of the components in the Noether- Lefschetz locus this construction is sufficient to generate an infinite dimensional subspace of the rational Griffiths group. For certain families of Calabi-Yau 3-folds, including the intersection of two general cubics, this is explicitly verified.

MSC:
14J30 \(3\)-folds
14C25 Algebraic cycles
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