“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)
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.
