Description

Book Synopsis
This monograph studies decompositions of the Jacobian of a smooth projective curve, induced by the action of a finite group, into a product of abelian subvarieties. The authors give a general theorem on how to decompose the Jacobian which works in many cases and apply it for several groups, as for groups of small order and some series of groups. In many cases, these components are given by Prym varieties of pairs of subcovers. As a consequence, new proofs are obtained for the classical bigonal and trigonal constructions which have the advantage to generalize to more general situations. Several isogenies between Prym varieties also result.




Trade Review
“The book is very well written, and gives a number of results, and of examples, interesting in some fields of Algebraic Geometry, specially those concerning algebraic curves, or equivalently, Riemann surfaces. Also, it serves to recall the work of Sevín Recillas Pishmish, whose untimely death prevented him from continuing working on these topics.” (José Javier Etayo, zbMATH 1514.14001, 2023)

Table of Contents
Introduction.- Preliminaries and basic results.- Finite covers of curves.- Covers of degree 2 and 3.- Covers of degree 4.- Some special groups and complete decomposabality.- Bibliography.- Index.

Decomposition of Jacobians by Prym Varieties

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    A Paperback / softback by Herbert Lange, Rubí E. Rodríguez

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      Book details

      Publisher Springer International Publishing AG
      Published 25 November 2022
      ISBN-13 9783031101441
      978-3031101441
      ISBN-10 3031101448
      Also in:
      Mathematics Algebraic geometry Complex analysis, complex variables

      Description

      Book Synopsis
      This monograph studies decompositions of the Jacobian of a smooth projective curve, induced by the action of a finite group, into a product of abelian subvarieties. The authors give a general theorem on how to decompose the Jacobian which works in many cases and apply it for several groups, as for groups of small order and some series of groups. In many cases, these components are given by Prym varieties of pairs of subcovers. As a consequence, new proofs are obtained for the classical bigonal and trigonal constructions which have the advantage to generalize to more general situations. Several isogenies between Prym varieties also result.




      Trade Review
      “The book is very well written, and gives a number of results, and of examples, interesting in some fields of Algebraic Geometry, specially those concerning algebraic curves, or equivalently, Riemann surfaces. Also, it serves to recall the work of Sevín Recillas Pishmish, whose untimely death prevented him from continuing working on these topics.” (José Javier Etayo, zbMATH 1514.14001, 2023)

      Table of Contents
      Introduction.- Preliminaries and basic results.- Finite covers of curves.- Covers of degree 2 and 3.- Covers of degree 4.- Some special groups and complete decomposabality.- Bibliography.- Index.

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