Decomposition of Jacobians by Prym Varieties
1st Edition
Published on 25. November 2022
Book
Paperback/Softback
XIII, 251 pages
978-3-031-10144-1 (ISBN)
Description
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.
Reviews / Votes
"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)More details
Product info
Paperback
Series
Edition
1st ed. 2022
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Professional and scholarly
Illustrations
67
67 s/w Abbildungen
XIII, 251 p. 67 illus.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 15 mm
Weight
411 gr
ISBN-13
978-3-031-10144-1 (9783031101441)
DOI
10.1007/978-3-031-10145-8
Schweitzer Classification
Other editions
Additional editions
Herbert Lange | Rubí E. Rodríguez
Decomposition of Jacobians by Prym Varieties
E-Book
11/2022
Springer
€69.54
Available for download
Persons
Herbert Lange
is a retired professor at the university of Erlangen-Nuremberg. His main research interests are abelian varieties and vector bundles on algebraic curves. He is the coauthor of several books, among them the Grundlehren volume "Complex Abelian Varieties" and for the series Progress in Mathematics, "Complex Tori".
RUB
Í E. RODR
ÍGUEZ
is Professor of Mathematics at Universidad de La Frontera and Director of the Geometry at the Frontier Research Center. Her research interests include moduli spaces of curves and abelian varieties, with special attention to the action of groups and algebras.
Content
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.