Products of Jacobians as Prym-Tyurin varieties

Abstract

Let $X_1,...,X_m$ denote smooth projective curves of genus $g_i\ge 2$ over an algebraically closed field of characteristic 0 and let $n$ denote any integer at least equal to $1+{\max }_{i=1}^m{g}_i$. We show that the product $J{X}_1\times ...\times J{X}_m$ of the corresponding Jacobian varieties admits the structure of a Prym-Tyurin variety of exponent $n^{m-1}$. This exponent is considerably smaller than the exponent of the structure of a Prym-Tyurin variety known to exist for an arbitrary principally polarized abelian variety. Moreover it is given by explicit correspondences.

13 pages

References in corpus (1)

• Prym-Tyurin varieties via Hecke algebras