Data for Shimura varieties intersecting the Torelli locus

TL;DR

This paper presents a method to identify the integral PEL datum of Shimura varieties containing images of Hurwitz spaces of cyclic covers under the Torelli morphism.

Contribution

It introduces a novel approach to determine the PEL datum for Shimura varieties associated with specific Hurwitz spaces.

Findings

Method applicable to infinitely many Hurwitz spaces of cyclic covers

Enables explicit determination of the Shimura variety's PEL datum

Bridges the study of Hurwitz spaces and Shimura varieties

Abstract

For infinitely many Hurwitz spaces parametrizing cyclic covers of the projective line, we provide a method to determine the integral PEL datum of the Shimura variety that contains the image of the Hurwitz space under the Torelli morphism.