Decomposition of Jacobians by Prym Varieties

1st ed. 2022

by Herbert Lange , Rubi E. Rodriguez

Book Details

Format Paperback / Softback

Book Series Lecture Notes in Mathematics

ISBN-10 3031101448

ISBN-13 9783031101441

Edition 1st ed. 2022

Publisher Springer International Publishing AG

Imprint Springer International Publishing AG

Country of Manufacture GB

Country of Publication GB

Publication Date Nov 25th, 2022

Print length 251 Pages

Weight 412 grams

Dimensions 15.50 x 23.20 x 1.90 cms

Product Classification: Complex analysis, complex variables Algebraic geometry

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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.

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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