m at h . A G ] 1 8 A ug 2 00 8 PRYM - TYURIN VARIETIES VIA HECKE ALGEBRAS

Let G denote a finite group and π : Z → Y a Galois covering of smooth projective curves with Galois group G. For every subgroup H of G there is a canonical action of the corresponding Hecke algebra Q[H\G/H ] on the Jacobian of the curve X = Z/H . To each rational irreducible representation W of G we associate an idempotent in the Hecke algebra, which induces a correspondence of the curve X and thus an abelian subvariety P of the Jacobian JX . We give sufficient conditions on W , H , and the action of G on Z for P to be a Prym-Tyurin variety. We obtain many new families of Prym-Tyurin varieties of arbitrary exponent in this way.