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Decomposition of Jacobians by Prym v...

Lange, H.

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Decomposition of Jacobians by Prym varieties

Record Type:	Electronic resources : Monograph/item
Title/Author:	Decomposition of Jacobians by Prym varieties/ by 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.
[NT 15003449]:	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.
Contained By:	Springer Nature eBook
Subject:	Jacobians. -
Online resource:	https://doi.org/10.1007/978-3-031-10145-8
ISBN:	9783031101458

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 ;v. 2310..

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

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

661654
Jacobians.

LC Class. No.: QA564

Dewey Class. No.: 516.35

Decomposition of Jacobians by Prym varieties
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245 1 0 $a Decomposition of Jacobians by Prym varieties $h [electronic resource] / $c by Herbert Lange, Rubi E. Rodriguez.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2022.
300 $a xiii, 251 p. : $b ill., digital ; $c 24 cm.
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.
650 0 $a Jacobians. $3 661654
650 0 $a Geometry, Algebraic. $3 532048
650 0 $a Curves, Algebraic. $3 540522
700 1 $a Rodriguez, Rubi E. $3 3609322
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Lecture notes in mathematics ; $v v. 2310. $3 3609323
856 4 0 $u https://doi.org/10.1007/978-3-031-10145-8
950 $a Mathematics and Statistics (SpringerNature-11649)