Rational and homological equivalence for real cycles.
If denotes the variety of irreducible plane curves of degree with exactly nodes as singularities, Diaz and Harris (1986) have conjectured that is a torsion group. In this note we study rational equivalence on some families of singular plane curves and we prove, in particular, that is a finite group, so that the conjecture holds for . Actually the order of is , the group being cyclic if is odd and the product of and a cyclic group of order if is even.
A relativization of earlier constructions and Nori’s rational Lefschetz theorem enable interesting examples of the “topological filtration” on algebraic cycles.
The purpose of this paper is to give a characterization of the relative tangent cone of two analytic curves in with an isolated intersection.