Abstract
Let Z be an algebraic p cycle homologous to zero in an algebraic complex manifold V. Associated to Z is a linear function ν 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 ν 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.
Keywords: algebraic cycle, integral, Fermat curve
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