2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61610Let G be a finite group acting on a smooth projective curve X. This induces an action of G on the Jacobian JX of X and thus a decomposition of JX up to isogeny. The most prominent example of such a situation is the group G of two elements. Let X --> Y denote the corresponding quotient map. Then JX is isogenous to the product of JY with the Prym variety of X/Y. In this paper some general results on group actions on abelian varieties are given and applied to deduce a decomposition of the jacobian JX for arbitrary group actions. Several examples are given.30 pages, corrected version abbriviated to 21 pages, to appear in Journ. Reine Angew. MathemAlgebraic Geometry14K05;14H40text