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＜E-Book＞
Decomposition of Jacobians by Prym Varieties / by Herbert Lange, Rubí E. Rodríguez
(Lecture Notes in Mathematics. ISSN:16179692 ; 2310)

Edition	1st ed. 2022.
Publisher	(Cham : Springer International Publishing : Imprint: Springer)
Year	2022
Size	XIII, 251 p. 67 illus : online resource
Authors	*Lange, Herbert author Rodríguez, Rubí E author SpringerLink (Online service)
Subjects	LCSH:Algebraic geometry LCSH:Functions of complex variables FREE:Algebraic Geometry FREE:Several Complex Variables and Analytic Spaces
Notes	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 HTTP:URL=https://doi.org/10.1007/978-3-031-10145-8

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