Abelian varieties with group action
Abstract
Description
Let 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. Mathem
30 pages, corrected version abbriviated to 21 pages, to appear in Journ. Reine Angew. Mathem