# 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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