2003/05/23 by Angel Carocca, Ángel Carocca, Rubí E. Rodríguez +3
Mathematics · #14H40 #20C05 #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #math.AG #msc:14H40 #msc:20C05
paper · pdf · doi:10.48550/arxiv.math/0305328
21 pages
arxiv created 2003/05/23 · openalex publication_date 2003/05/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The object of this paper is to prove some general results about rational idempotents for a finite group G and deduce from them geometric information about the components that appear in the decomposition of the Jacobian variety of a curve with G-action. We give an algorithm to find explicit primitive rational idempotents for any G, as well as for rational projectors invariant under any given subgroup. These explicit constructions allow geometric descriptions of the factors appearing in the decomposition of a Jacobian with group action: from them we deduce the decomposition of any Prym or Jacobian variety of an intermediate cover, in the case of a Jacobian with G-action. In particular, we give a necessary and sufficient condition for a Prym variety of an intermediate cover to be such a factor.