Decomposition of Jacobians by Prym Varieties (Lecture Notes in Mathematics, Band 2310) - Softcover

Lange, Herbert; Rodríguez, Rubí E.

Softcover

ISBN 10: 3031101448 ISBN 13: 9783031101441

Verlag: Springer, 2022

Inhaltsangabe

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.

Über diesen Titel

Über die Autorin bzw. den Autor

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.

Von der hinteren Coverseite

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.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2022
• Sprache: Englisch
• ISBN 10: 3031101448
• ISBN 13: 9783031101441
• Einband: Taschenbuch
• Auflage: 1
• Anzahl der Seiten: 268
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