On Shimura subvarieties of the Prym locus

TL;DR

This paper demonstrates that certain families of Prym varieties derived from abelian Galois covers of the projective line do not form high-dimensional Shimura subvarieties in the moduli space of abelian varieties.

Contribution

It establishes a non-existence result for high-dimensional Shimura subvarieties arising from Prym loci of abelian Galois covers.

Findings

Families of Pryms from abelian Galois covers do not produce high-dimensional Shimura subvarieties.

The result applies to covers in both $A_{g-1}$ and $A_g$ moduli spaces.

Provides new insights into the structure of Prym loci and their relation to Shimura varieties.

Abstract

We show that families of Pryms of abelian Galois covers of $\mathbb{P}^1$ in $A_{g-1}$ (resp. $A_g$) do not give rise to high dimensional Shimura subvareties.