A characterization of special subvarieties in orthogonal Shimura varieties

Stefan Müller-Stach; Kang Zuo

A characterization of special subvarieties in orthogonal Shimura varieties

Algebraic Geometry 2013-06-12 v3 Complex Variables Number Theory

Authors: Stefan Müller-Stach , Kang Zuo

Abstract

Let $Y$ be a subvariety contained in a smooth Mumford compactification of an orthogonal Shimura variety $M \subset A_g$ , where $A_g$ is the moduli space of principally polarized abelian varieties of dimension $g$ with some level structure, such that $Y$ intersects the boundary of $A_g$ transversally. Then we give necessary and sufficient conditions of Andr\'e-Oort type for $Y$ itself being the compactification of a special subvariety $Y^0 \subset M$

Keywords

orthogonal Shimura varieties special subvarieties André-Oort conjecture Mumford compactification abelian varieties

Cite

@article{arxiv.1008.5301,
  title  = {A characterization of special subvarieties in orthogonal Shimura varieties},
  author = {Stefan Müller-Stach and Kang Zuo},
  journal= {arXiv preprint arXiv:1008.5301},
  year   = {2013}
}

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A characterization of special subvarieties in orthogonal Shimura varieties

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