Homological versus algebraic equivalence in a jacobian.
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 algebraically equivalent to zero.
Mathematics Department, Brown University, Providence, Rhode Island 02912.
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Harris