We study Shimura (special) subvarieties in the moduli space Ap,D of complex abelian varieties of dimension p and polarization type D. These subvarieties arise from families of covers compatible with a fixed group action on the base curve such that the quotient of the base curve by the group is isomorphic to P1. We give a criterion for the image of these families under the Prym map to be a special subvariety and, using computer algebra, obtain 210 Shimura subvarieties contained in the Prym locus.
Grosselli, G., Mohajer, A. (2023). Shimura subvarieties in the Prym locus of ramified Galois coverings. COLLECTANEA MATHEMATICA, 74(1), 199-218 [10.1007/s13348-021-00342-5].
Shimura subvarieties in the Prym locus of ramified Galois coverings
Grosselli, G P;
2023
Abstract
We study Shimura (special) subvarieties in the moduli space Ap,D of complex abelian varieties of dimension p and polarization type D. These subvarieties arise from families of covers compatible with a fixed group action on the base curve such that the quotient of the base curve by the group is isomorphic to P1. We give a criterion for the image of these families under the Prym map to be a special subvariety and, using computer algebra, obtain 210 Shimura subvarieties contained in the Prym locus.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.