Decomposition of Jacobians by Prym Varieties
Buch in deiner Nähe kaufen
Beschreibung
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.
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.
Presents new proofs of the bigonal and trigonal constructions Includes previously unpublished material on covers of degree 4 Describes results that provide many examples that will be of interest to algebraic geometers
Autor*in
Herbert Lange
Themen in »Decomposition of Jacobians by Prym Varieties«
Complex abelian varieties Prym varieties Decomposition of Jacobian Coverings Abelian subvariety Classical bigonal and trigonal constructions
Stimmen zu »Decomposition of Jacobians by Prym Varieties«
“The Decompositions. The entire book is quite thorough, with enough background to serve as a standalone reference for several mini courses.” (John T. Cullinan, Mathematical Reviews, May, 2024)
“The book is very well written, and gives a number of results, and of examples, interesting in some fields of Algebraic Geometry, specially those concerning algebraic curves, or equivalently, Riemann surfaces. Also, it serves to recall the work of Sevín Recillas Pishmish, whose untimely death prevented him from continuing working on these topics.” (José Javier Etayo, zbMATH 1514.14001, 2023)
()