Shimura subvarieties in the Prym locus of ramified Galois coverings

Grosselli, Gian Paolo ^[1] ; Mohajer, Abolfazl ^[2]
1. [1] Dipartimento di Matematica, Università di Pavia, Via Ferrata 5, 27100, Pavia, Italy
2. [2] Institut für Mathematik, Fachbereich 08, Universität Mainz, 55099, Mainz, Germany
Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 74, Fasc. 1, 2023, págs. 199-218
Idioma: inglés
DOI: 10.1007/s13348-021-00342-5
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Resumen
- 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.