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Decomposition of Jacobians by Prym varieties

Record Type:	Electronic resources : Monograph/item
Title/Author:	Decomposition of Jacobians by Prym varietiesby Herbert Lange, Rubi E. Rodriguez.
Author:	Lange, H.
other author:	Rodriguez, Rubi E.
Published:	Cham :Springer International Publishing :2022.
Description:	xiii, 251 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Jacobians.
Online resource:	https://doi.org/10.1007/978-3-031-10145-8
ISBN:	9783031101458$q(electronic bk.)

Decomposition of Jacobians by Prym varieties
Lange, H.

Decomposition of Jacobians by Prym varieties[electronic resource] /by Herbert Lange, Rubi E. Rodriguez. - Cham :Springer International Publishing :2022. - xiii, 251 p. :ill., digital ;24 cm. - Lecture notes in mathematics,v. 23101617-9692 ;. - Lecture notes in mathematics ;2035..

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.

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.

ISBN: 9783031101458$q(electronic bk.)

Standard No.: 10.1007/978-3-031-10145-8doiSubjects--Topical Terms:

740390
Jacobians.

LC Class. No.: QA564

Dewey Class. No.: 516.35

Decomposition of Jacobians by Prym varieties
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490 1 $a Lecture notes in mathematics, $x 1617-9692 ; $v v. 2310
505 0 $a 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.
520 $a 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.
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