Prym-Tyurin varieties using self-products of groups

Details Prym-Tyurin varieties using self-products of groups Prym-Tyurin varieties using self-products of groups

2008-05-30

arxiv.org/abs/0805.4782v1

Mathematics

Algebraic Geometry

23 pages

Scientific paper

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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