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arXiv · 0805.4785

Products of Jacobians as Prym-Tyurin varieties

A. Carocca·H. Lange·R. E. Rodriguez·A. M. Rojas
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Abstract

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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A. Carocca, H. Lange, R. E. Rodriguez, A. M. Rojas. 2008-05-30. Products of Jacobians as Prym-Tyurin varieties. https://arxiv.org/abs/0805.4785

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