| A classical problem has been to study and describe the geometry of the moduli space of principally polarized abelian varieties (ppavs). A useful point of view is to study abelian varieties via curve theory. Two special classes of ppavs coming from curves are Jacobians and classical Prym varieties. In dimension 2 and 3, a generic ppav is a Jacobian variety and in dimension 4 and 5 a generic ppav is a classical Prym variety. A generalization of these varieties are Prym-Tyurin varieties of exponent q. The Prym-Tyurin varieties of exponent 1 and 2 are precisely Jacobians and classical Pryms. A problem to understand these varieties in terms of curves as well as we understand Jacobians and classical Prym varieties has been that there are not many known examples for small exponent greater or equal to 3. In this talk I will present new examples of Prym-Tyurin varieties of exponent 3 and 4 that appear as isotypical components of Jacobian varieties. |
