English

On the Abel-Jacobi maps of Fermat Jacobians

Algebraic Geometry 2010-03-02 v1 Number Theory

Abstract

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

Keywords

Cite

@article{arxiv.1003.0357,
  title  = {On the Abel-Jacobi maps of Fermat Jacobians},
  author = {Noriyuki Otsubo},
  journal= {arXiv preprint arXiv:1003.0357},
  year   = {2010}
}