On Shimura subvarieties generated by families of abelian covers of ${\mathbb{P}}^1$

Abstract

We study the locus of abelian Galois covers of ${\mathbb{P}}^1$ in $A_g$ and the problem of occurrence of Shimura (special) subvarieties generated by these covers in the Torelli locus $T_g$ inside $A_g$. We first investigate the existence of Shimura subvarieties in the mentioned locus by some computational methods based on Moonen-Oort works and then exclude many cases using both characteristic $p$ methods and monodromy computations.

23 pages

References in corpus (1)

• On Shimura curves in the Torelli locus of curves