On the Abel-Jacobi maps of Fermat Jacobians
Abstract
We study the Abel-Jacobi image of the Ceresa cycle Wk-Wk-, where Wk is the image of the k-th symmetric product of a curve X on its Jacobian variety. For the Fermat curve of degree N, we express it in terms of special values of generalized hypergeometric functions and give a criterion for the non-vanishing of Wk-Wk- modulo algebraic equivalence, which is verified numerically for some N and k.
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