We study Shimura curves of PEL type in the space of polarised abelian varieties generically contained in the ramified Prym locus. We generalise to ramified double covers, the construction done by the first author with Colombo, Ghigi and Penegini 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 the projective line. Using computer algebra we obtain 184 Shimura curves contained in the (ramified) Prym loci.
Shimura curves in the Prym loci of ramified double covers
Frediani Paola;
2021-01-01
Abstract
We study Shimura curves of PEL type in the space of polarised abelian varieties generically contained in the ramified Prym locus. We generalise to ramified double covers, the construction done by the first author with Colombo, Ghigi and Penegini 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 the projective line. Using computer algebra we obtain 184 Shimura curves contained in the (ramified) Prym loci.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
