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arXiv · 0805.4782

Prym-Tyurin varieties using self-products of groups

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

Given Prym-Tyurin varieties of exponent $q$ with respect to a finite group $G$, a subgroup $H$ and a set of rational irreducible representations of $G$ satisfying some additional properties, we construct a Prym-Tyurin variety of exponent $[G:H]q$ in a natural way. We study an example of this result, starting from the dihedral group $\mathbf{D}_p$ for any odd prime $p$. This generalizes the construction of arXiv:math/0412103v2[math.AG] for $p=3$. Finally, we compute the isogeny decomposition of the Jacobian of the curve underlying the above mentioned example.

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A. Carocca, H. Lange, R. E. Rodriguez, A. M. Rojas. 2008-05-30. Prym-Tyurin varieties using self-products of groups. https://arxiv.org/abs/0805.4782

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