A characterization of special subvarieties in orthogonal Shimura varieties

Details A characterization of special subvarieties in orthogonal Shimura varieties A characterization of special subvarieties in orthogonal Shimura varieties

2010-08-31

arxiv.org/abs/1008.5301v2

Mathematics

Algebraic Geometry

largely revised

Scientific paper

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 $Y^0 \subset M$

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