Group actions on Jacobian varieties

  • Anita M. Rojas

    Universidad de Chile, Santiago, Chile


Consider a finite group acting on a Riemann surface , and the associated branched Galois cover . We introduce the concept of \emph{geometric signature} for the action of , and we show that it captures much information: the geometric structure of the lattice of intermediate covers, the isotypical decomposition of the rational representation of the group acting on the Jacobian variety of , and the dimension of the subvarieties of the isogeny decomposition of . We also give a version of Riemann's existence theorem, adjusted to the present setting.

Cite this article

Anita M. Rojas, Group actions on Jacobian varieties. Rev. Mat. Iberoam. 23 (2007), no. 2, pp. 397–420

DOI 10.4171/RMI/500