# On the Abel–Jacobi maps of Fermat Jacobians

@article{Otsubo2010OnTA, title={On the Abel–Jacobi maps of Fermat Jacobians}, author={Noriyuki Otsubo}, journal={Mathematische Zeitschrift}, year={2010}, volume={270}, pages={423-444} }

We study the Abel–Jacobi image of the Ceresa cycle $${W_k-W_k^-}$$, where Wk is the image of the kth 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 $${W_k-W_k^-}$$ modulo algebraic equivalence, which is verified numerically for some N and k.

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