Homological versus algebraic equivalence in a jacobian.

@article{Harris1983HomologicalVA,
title={Homological versus algebraic equivalence in a jacobian.},
author={Brian Harris},
journal={Proceedings of the National Academy of Sciences of the United States of America},
year={1983},
volume={80 4},
pages={1157-8}
}

Let Z be an algebraic p cycle homologous to zero in an algebraic complex manifold V. Associated to Z is a linear function nu on holomorphic (2p + 1)-forms on V, modulo periods, that vanishes if Z is algebraically equivalent to zero in V. I give a formula for nu for the case of V the jacobian of an algebraic curve C and Z=C - C' (C' = "inverse" of C') in terms of iterated integrals of holomorphic 1-forms on C. If C is the degree 4 Fermat curve, I use this formula to show that C - C' is not… CONTINUE READING