Shimura curves in the Prym loci of ramified double covers

Paola Frediani; Gian Paolo Grosselli

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arXiv · 2007.09646

Shimura curves in the Prym loci of ramified double covers

Paola Frediani·Gian Paolo Grosselli

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Abstract

We study Shimura curves of PEL type in the space of polarised abelian varieties $A^{\delta}_p$ generically contained in the ramified Prym locus. We generalise to ramified double covers, the construction done in [10] in the unramified case and in the case of two ramification points. Namely, we construct families of double covers which are compatible with a fixed group action on the base curve. We only consider the case of one-dimensional families and where the quotient of the base curve by the group is ${\mathbb P}^1$. Using computer algebra we obtain 184 Shimura curves contained in the (ramified) Prym loci.

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Paola Frediani, Gian Paolo Grosselli. 2020-07-19. Shimura curves in the Prym loci of ramified double covers. https://arxiv.org/abs/2007.09646

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