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

2016/09/06 by Milagros Izquierdo, M. Izquierdo, Izquierdo, M. +6
Mathematics · #14H37 #14H40 #14H55 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #math.AG #msc:14H37 #msc:14H40 #msc:14H55

paper · pdf · doi:10.48550/arxiv.1609.01562

24 figures, 9 tables

arxiv created 2016/09/06 · openalex publication_date 2016/09/06 · arxiv updated 2016/09/07 · openalex created_date 2016/09/16 · openalex updated_date 2026/07/28

Abstract

Given a compact Riemann surface X with an action of a finite group G, the group algebra Q[G] provides an isogenous decomposition of its Jacobian variety JX, known as the group algebra decomposition of JX. We consider the set of equisymmetric Riemann surfaces M(2n-1, D_2n, θ) for all n≥ 2. We study the group algebra decomposition of the Jacobian JX of every curve X∈ M(2n-1, D_2n,θ) 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 JX as Jacobian (or Prym) varieties of intermediate coverings. Finally, we compute the dimension of the corresponding Shimura domains.

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