A characterization of special subvarieties in orthogonal Shimura varieties

2010/08/31 by Stefan Müller–Stach, Kang Zuo, Müller-Stach, Stefan +1 · 1 citation
Mathematics · #14G35 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1008.5301

openalex publication_date 2010/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Y be a subvariety contained in a smooth Mumford compactification of an orthogonal Shimura variety M ⊂ 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 André-Oort type for Y itself being the compactification of a special subvariety Y⁰ ⊂ M

Cited by

• Special subvarieties in Mumford-Tate varieties

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• Oort's conjecture for A_g