2003/03/12 by Sevin Recillas, Sevín Recillas, Rubí E. Rodríguez +3 · 1 citation
Mathematics · #14H37 #14H40 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #math.AG #msc:14H37 #msc:14H40
paper · pdf · doi:10.48550/arxiv.math/0303155
77 pages
arxiv created 2003/03/12 · openalex publication_date 2003/03/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We describe the isotypical decomposition of the Jacobian variety JW of the Galois extension W-->T of any fourfold cover of smooth connected irreducible projective complex curves X-->T, in terms of Prym's of intermediate covers. We also compute the degree of the isogenies involved and as a result we obtain new proofs of the bigonal and trigonal constructions. Furthermore, we give examples of families of Jacobians isogenous to a product of Jacobians and of families of Prym varieties isogenous to the product of elliptic curves.