Decomposition of Jacobian varieties of curves with dihedral actions via equisymmetric stratification

  • Milagros Izquierdo

    Linköping University, Sweden
  • Leslie Jiménez

    Linköping University, Sweden and Universidad de Chile, Santiago, Chile
  • Anita M. Rojas

    Universidad de Chile, Santiago, Chile
Decomposition of Jacobian varieties of curves with dihedral actions via equisymmetric stratification cover

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Abstract

Given a compact Riemann surface with an action of a finite group , the group algebra provides an isogenous decomposition of its Jacobian variety , known as the group algebra decomposition of . We consider the set of equisymmetric Riemann surfaces for all . We study the group algebra decomposition of the Jacobian of every curve for all admissible actions, and we provide affine models for them. We use the topological equivalence of actions on the curves to obtain facts regarding its Jacobians. We describe some of the factors of as Jacobian (or Prym) varieties of intermediate coverings. Finally, we compute the dimension of the corresponding Shimura domains.

Cite this article

Milagros Izquierdo, Leslie Jiménez, Anita M. Rojas, Decomposition of Jacobian varieties of curves with dihedral actions via equisymmetric stratification. Rev. Mat. Iberoam. 35 (2019), no. 4, pp. 1259–1279

DOI 10.4171/RMI/1084