Jacobians with group actions and rational idempotents
arXiv:math/0305328
Abstract
The object of this paper is to prove some general results about rational idempotents for a finite group and deduce from them geometric information about the components that appear in the decomposition of the Jacobian variety of a curve with action. We give an algorithm to find explicit primitive rational idempotents for any , 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 action. In particular, we give a necessary and sufficient condition for a Prym variety of an intermediate cover to be such a factor.
21 pages