Correspondences with split polynomial equations

Abstract

We introduce endomorphisms of special jacobians and show that they satisfy polynomial equations with all integer roots which we compute. The eigen-abelian varieties for these endomorphisms are generalizations of Prym-Tjurin varieties and naturally contain special curves representing cohomology classes which are not expected to be represented by curves in generic abelian varieties.

arXiv commentAMS-Latex, 32 pages, minor corrections, computation of dimensions of eigen-abelian varieties added