The fundamental group of the complement of the singular locus of Lauricella's $F_C$

Yoshiaki Goto, Jyoichi Kaneko

Published 2017-10-26Version 1

We study the fundamental group of the complement of the singular locus of Lauricella's hypergeometric function $F_C$ of $n$ variables. The singular locus consists of $n$ hyperplanes and a hypersurface of degree $2^{n-1}$ in the complex $n$-space. We give a conjectural presentation of the fundamental group, and prove it in the three-dimensional case. We also consider a presentation of the fundamental group of $2^3$-covering of this space.