Some remarks on algebraic equivalence of cycles.Pacific J. Math. 105 (1983), no. 2, 285–290.

This paper deals with algebraic equivalence of homologous algebraic cycles in certain threefolds. Specifically it is shown that: (a) In the blow-up at the node of a general 3-fold in P4 with a single ordinary node, the lines of the two rulings of the exceptional divisor are homologous but not algebraically equivalent; (b) on a general quintic 3-foldW in P4, two lines, although homologous, are not algebraically equivalent. In fact, the argument shows that they do not differ by a torsion element of the group of cycles modulo algebraic equivalence, and hence that no nonzero linear combination of the 2875 lines onW is algebraically equivalent to zero. Reviewed by Joseph Harris