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Higher Dimensional Harmonic Volume Can be Computed as an Iterated Integral
Published online by Cambridge University Press: 20 November 2018
Abstract
In this paper it is shown that the computation of higher dimensional harmonic volume, defined in [1], can be reduced to Harris' computation in the onedimensional case (See [3]), so that higher dimensional harmonic volume may be computed essentially as an iterated integral. We then use this formula to produce a specific smooth curve , namely a specific double cover of the Fermat quartic, so that the image
of the second symmetric product of
in its Jacobian via the Abel-Jacobi map is algebraically inequivalent to the image of
under the group involution on the Jacobian.
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- Copyright © Canadian Mathematical Society 1992
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