We study the fundamental group of the complement of the singular locus ofLauricella's hypergeometric function $F_C$ of $n$ variables. The singular locusconsists of $n$ hyperplanes and a hypersurface of degree $2^{n-1}$ in thecomplex $n$-space. We derive some relations that holds for general $n\geq 3$.We give an explicit presentation of the fundamental groupin thethree-dimensional case. We also consider a presentation of the fundamentalgroup of $2^3$-covering of this space. In the version 2, we omit some of the calculations. For all the calculations,refer to the version 1 (arXiv:1710.09594v1) of this article.
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机译：我们研究了$ n $变量的Lauricella超几何函数$ F_C $的奇异轨迹补码的基本群。奇异轨迹由$ n $个超平面和一个复杂的$ n $空间中度数为$ 2 ^ {n-1} $的超曲面组成。我们推导了一些适用于一般$ n \ geq 3 $的关系。我们在三维情况下给出了基本群的明确表示。我们还考虑了这个空间的2 ^ 3 $基本群的介绍。在版本2中，我们省略了一些计算。有关所有计算，请参考本文的版本1（arXiv：1710.09594v1）。
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