Products of Jacobians as Prym-Tyurin varieties

Details Products of Jacobians as Prym-Tyurin varieties Products of Jacobians as Prym-Tyurin varieties

2008-05-30

arxiv.org/abs/0805.4785v1

Mathematics

Algebraic Geometry

13 pages

Scientific paper

Let $X_1, ..., X_m$ denote smooth projective curves of genus $g_i \geq 2$ 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 $JX_1 \times ... \times JX_m$ 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.

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