Die Fundamentalgruppen der Siegelschen Modulvarietäten. (The fundamental groups of the Siegel varieties of moduli) (Q1821922)

We show by toroidal methods that Satake's compactification of \(S_ n/\Gamma _ n(\lambda)\) as well as any desingularisation is simply connected for \(n\geq 2\), \(\lambda\) \(\geq 3\). Here \(S_ n\) is Siegel's upper half plane of degree n and \(\Gamma _ n(\lambda)\) the congruence subgroup of level \(\lambda\) in \(Sp_ n{\mathbb{Z}}\).