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Algebraic cycles on a general complete intersection of high multi-degree of a smooth projective variety. (English) Zbl 0882.14001

Our goal in this paper is to generalize the results of M. L. Green [J. Differ. Geom. 29, No. 3, 545-555 (1989; Zbl 0692.14003)] and C. Voisin [C. R. Acad. Sci., Paris, Sér. I 307, No. 4, 157-160 (1988; Zbl 0673.14005)] on the Abel-Jacobi map for general 3-folds of degree \(d\geq 6\) in \(\mathbb{P}^4\) to arbitrary general complete intersections of high multi-degrees on any smooth projective variety. Our work on this was highly influenced by conversations with M. Nori [cf. M. V. Nori, Invent. Math. 111, No. 2, 349-373 (1993; Zbl 0822.14008)]. We have phrased our result in terms of rational Deligne cohomology.

MSC:

14C25 Algebraic cycles
14M10 Complete intersections
14F99 (Co)homology theory in algebraic geometry
14C05 Parametrization (Chow and Hilbert schemes)
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References:

[1] Green, M. : Griffiths’ infinitesimal invariant and the Abel-Jacobi map , Journal of Diff. Geometry 29 (1989), 545-555. · Zbl 0692.14003
[2] Nori, M. : Algebraic cycles and Hodge theoretic connectivity , Inv. Math 111 (1993), 349-373. · Zbl 0822.14008
[3] Paranjape, K. : Cohomological and cycle-theoretic connectivity , preprint (1992). · Zbl 0828.14003
[4] Ravi, M. : An effective version of Nori’s theorem , preprint (1992). · Zbl 0790.14005
[5] Voisin, C. : Une remarque sur l’invariant infinitésimal des fonctions normales , C.R. Acad. Sci. Paris t. 307 (1988), 157-160. · Zbl 0673.14005
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