Decomposition of Jacobians by Prym Varieties / by Herbert Lange, Rubí E. Rodríguez.

Format:

Book

Author/Creator:

Lange, Herbert., Author.

Rodríguez, Rubí E., Author.

Contributor:

SpringerLink (Online service)

Series:

Mathematics and Statistics (SpringerNature-11649)

Lecture Notes in Mathematics, 1617-9692 ; 2310

Language:

English

Subjects (All):

Geometry, Algebraic.

Functions of complex variables.

Algebraic Geometry.

Several Complex Variables and Analytic Spaces.

Local Subjects:

Algebraic Geometry.

Several Complex Variables and Analytic Spaces.

Physical Description:

1 online resource (XIII, 251 pages) : 67 illustrations

Edition:

1st edition 2022.

Contained In:

Springer Nature eBook

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2022.

System Details:

text file PDF

Summary:

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.

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.

Other Format:

Printed edition:

ISBN:

978-3-031-10145-8

9783031101458

Access Restriction:

Restricted for use by site license.