Die Fundamentalgruppen Siegelscher Modulvarietäten. (The fundamental groups of Siegel modular varieties) (Q752787)

Let \(\Gamma\) be a subgroup of finite index of the Siegel modular group \(Sp(g,{\mathbb{Z}})\) of degree \(g\geq 2.\) It acts on the so-called Siegel half plane \(S_ g\). Let Y be any normal proper modification of the Satake- compactification of \(S_ g/\Gamma\). The author proves: * If \(\Gamma\) is a principal congruence subgroup of arbitrary level \(\lambda\geq 1\), then Y is simply connected. * The fundamental group of Y is always finite. These results are based on a paper by \textit{J. Mennicke} [Math. Ann. 159, 115-129 (1965; Zbl 0134.265)].