Abelian varieties with group action

Details Abelian varieties with group action Abelian varieties with group action

2001-06-08

arxiv.org/abs/math/0106055v2

Mathematics

Algebraic Geometry

30 pages, corrected version abbriviated to 21 pages, to appear in Journ. Reine Angew. Mathem

Scientific paper

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.

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