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

and an appendix of detailed calculations

Yoshiaki Goto and Jyoichi Kaneko

Note that errata exists for this article.

Journal of Singularities
volume 17 (2018), 295-329

Received: 30 January 2018. Received in revised form: 28 July 2018

DOI: 10.5427/jsing.2018.17m

Add a reference to this article to your citeulike library.

Abstract:

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 derive some relations that hold for general n ≥ 3. We give an explicit presentation of the fundamental group in the three-dimensional case. We also consider a presentation of the fundamental group of 2^3-covering of this space.

Keywords:

Fundamental groups, van Kampen-Zariski theorem, Reidemeister-Schreier method, Lauricella's F_C

Mathematical Subject Classification (2010):

14F35, 57M05, 57M10

Author(s) information:

Yoshiaki Goto	Jyoichi Kaneko
General Education	Department of Mathematical Sciences
Otaru University of Commerce	University of the Ryukyus
Otaru, Hokkaido, 047-8501, Japan	Nishihara, Okinawa, 903-0213, Japan
email: goto@res.otaru-uc.ac.jp	email: kaneko@math.u-ryukyu.ac.jp