Overview
- Authors:
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Herbert Lange
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Department Mathematik, University of Erlangen-Nuremberg, Erlangen, Germany
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Rubí E. Rodríguez
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Department of Mathematics, Universidad de La Frontera, Temuco, Chile
- Presents new proofs of the bigonal and trigonal constructions
- Includes previously unpublished material on covers of degree 4
- Describes results that provide many examples that will be of interest to algebraic geometers
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Table of contents (7 chapters)
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Front Matter
Pages i-xiii
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- Herbert Lange, Rubí E. Rodríguez
Pages 1-5
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- Herbert Lange, Rubí E. Rodríguez
Pages 7-38
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- Herbert Lange, Rubí E. Rodríguez
Pages 39-78
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- Herbert Lange, Rubí E. Rodríguez
Pages 79-94
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- Herbert Lange, Rubí E. Rodríguez
Pages 95-172
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- Herbert Lange, Rubí E. Rodríguez
Pages 173-220
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- Herbert Lange, Rubí E. Rodríguez
Pages 221-246
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Back Matter
Pages 247-251
About this book
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
“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)
Authors and Affiliations
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Department Mathematik, University of Erlangen-Nuremberg, Erlangen, Germany
Herbert Lange
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Department of Mathematics, Universidad de La Frontera, Temuco, Chile
Rubí E. Rodríguez
About the authors
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".
RUBÍ E. RODRÍGUEZ 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.
