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

Abolfazl Mohajer; Kang Zuo

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arXiv · 1402.1900

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

Abolfazl Mohajer·Kang Zuo

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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.

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BibTeX RIS

Abolfazl Mohajer, Kang Zuo. 2014-02-08. On Shimura subvarieties generated by families of abelian covers of $\mathbb{P}^{1}$. https://arxiv.org/abs/1402.1900

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