On the Abel–Jacobi maps of Fermat Jacobians

Abstract

We study the Abel–Jacobi image of the Ceresa cycle $${W_k-W_k^-}$$ , where W k 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.