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Abelian varieties with group action

H. Lange·S. Recillas
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Abstract

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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H. Lange, S. Recillas. 2003-11-06. Abelian varieties with group action. https://arxiv.org/abs/math/0106055

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