JournalsrmiVol. 23, No. 2pp. 397–420

Group actions on Jacobian varieties

  • Anita M. Rojas

    Universidad de Chile, Santiago, Chile
Group actions on Jacobian varieties cover
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Consider a finite group GG acting on a Riemann surface SS, and the associated branched Galois cover πG:SY=S/G\pi_G:S \to Y=S/G. We introduce the concept of \emph{geometric signature} for the action of GG, 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 GG acting on the Jacobian variety JSJS of SS, and the dimension of the subvarieties of the isogeny decomposition of JSJS. We also give a version of Riemann's existence theorem, adjusted to the present setting.

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

DOI 10.4171/RMI/500