Shimura subvarieties in the Prym locus of ramified Galois coverings

2021/06/10 by Grosselli, Gian Paolo, Mohajer, Abolfazl
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2106.05704

Abstract

We study Shimura (special) subvarieties in the moduli space A_p,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.

Related

• Higher dimensional Shimura varieties in the Prym loci of ramified double covers
• Families of Prym varieties of abelian coverings and Shimura varieties
• Shimura curves in the Prym loci of ramified double covers
• On Shimura subvarieties of the Prym locus
• On Shimura subvarieties generated by families of abelian covers of ℙ¹