Lawson homology for varieties with small Chow groups and the induced filtration on the Griffiths groups

Abstract

These groups form an intriguing set of invariants. Despite the vast literature on this subject, the groups have been calculated only in very few cases, such as for the projective spaces. One of the goals of this note is to understand these invariants in case the variety has “few cycles” in the sense that rational and homological equivalence coincide for all m-cycles up to a certain rank m = s. Actually, the results only deal with that part of Lawson homology that is not “visible” in ordinary homology in that it is in the kernel of the cycle class maps cm,k+2m : LmHk+2m(X)→ Hk+2m(X),