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Die Fundamental Gruppen Siegelscher Modul Varietäten

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Abstract

Let Γ be a subgroup of finite index of Siegels modular group Γg = Sp(g,Z) and Y(Γ) a proper modification of the Satake compactification (Sg/Γ)* of Siegels modular space Sg/Γ of degree g≧2.

It will be shown that Y(Γ) is simply connected for all principal congruence subgroups Γ = Γg(λ). Moreover the fundamental group of Y is always finite. These results are based on J. Mennickes work showing that Γg(λ) is the normal hull in Γg of a single matrix μg(λ).

Secondly it will be proved that for g=2,3 and λ≧3 this fact is even equivalent to the simply connectedness of any desingularisation of (Sg/Γg(λ)).

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  1. Holger Heidrich-Riske, Untergasse 1, 3572, Amöneburg

    Holger Heidrich-Riske

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  1. Holger Heidrich-Riske
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Die vorliegende Arbeit wurde von der Hessischen Graduiertenförderung unterstützt.

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Heidrich-Riske, H. Die Fundamental Gruppen Siegelscher Modul Varietäten. Manuscripta Math 68, 161–189 (1990). https://doi.org/10.1007/BF02568758

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  • DOI: https://doi.org/10.1007/BF02568758

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