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Curves on threefolds with trivial canonical bundle. (English) Zbl 0759.14031
Summary: C. H. Clemens [Publ. Math., Inst. Haut. Étud. Sci. 58, 231-250 (1983; Zbl 0529.14002)] has shown that homologically trivial codimension two cycles on a general hypersurface of degree five and dimension three form a subgroup of infinite rank inside the intermediate jacobian. We generalize this to other complete intersection threefolds with trivial canonical bundle.

MSC:
14J30 \(3\)-folds
14K30 Picard schemes, higher Jacobians
14C25 Algebraic cycles
14H99 Curves in algebraic geometry
14M07 Low codimension problems in algebraic geometry
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