  This paper forms the major portion of a talk given at the International
Colloquium on Arithmetic, Algebra and Geometry at TIFR, Mumbai in Jan 2000. We
look at the problem of detecting cycles with trivial Abel-Jacobi invariant. M.
Green proposed a Hodge-theoretic method to which C. Voisin found a
counter-example. We present an easier example. We also propose another possible
invariant to detect these classes using Hodge Theory. Similar methods have been
proposed earlier by M. Asakura and M. Saito.
