On a geometric analogue of the Andre-Oort conjecture for the Zariski closure of positive-dimensional

来源 :International Conference on Complex Geometry, Singularities | 被引量 : 0次 | 上传用户:gigahunter
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  Let Ω be a bounded symmetric domain,Γ ∈Aut(Ω) be a torsion-free lattice,X:= Ω/Γ.Let∈ Z X be an irreducible quasi-projective variety such that Z is the Zariski closure of an infinite family of totally geodesic complex subvarieties Sa∈ Z,a∈ A.Under certain non-degeneracy conditions one expects Z to be also totally geodesic,so that Z is in particular again uniformized by a bounded symmetric domain.This set-up is related to the Andr′e-Oort Conjecture since (positive-dimensional) special varieties in the context of the latter conjecture are known to be totally geodesic.
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