Jacobians with group actions and rational idempotents

Details Jacobians with group actions and rational idempotents Jacobians with group actions and rational idempotents

2003-05-23

arxiv.org/abs/math/0305328v1

Mathematics

Algebraic Geometry

21 pages

Scientific paper

The object of this paper is to prove some general results about rational idempotents for a finite group $G$ and deduce from them geometric information about the components that appear in the decomposition of the Jacobian variety of a curve with $G-$action. We give an algorithm to find explicit primitive rational idempotents for any $G$, as well as for rational projectors invariant under any given subgroup. These explicit constructions allow geometric descriptions of the factors appearing in the decomposition of a Jacobian with group action: from them we deduce the decomposition of any Prym or Jacobian variety of an intermediate cover, in the case of a Jacobian with $G-$action. In particular, we give a necessary and sufficient condition for a Prym variety of an intermediate cover to be such a factor.

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