Deligne-Mostow theory

introduction

Deligne and Mostow constructed a class of lattices in PU(2,1) using monodromy of hypergeometric functions. Later, Thurston reinterpreted them in terms of cone metrics on the sphere.

Looijenga, Eduard. “Uniformization by Lauricella Functions--an Overview of the Theory of Deligne-Mostow.” arXiv:math/0507534, July 26, 2005. http://arxiv.org/abs/math/0507534.

V. Bytev, B. Kniehl, HYPERgeometric functions DIfferential REduction: Mathematica-based packages for the differential reduction of generalizedhypergeometric functions: Fc hypergeometric function of three variables, arXiv:1602.00917 [math-ph], February 02 2016, http://arxiv.org/abs/1602.00917
Selim Ghazouani, Luc Pirio, Moduli spaces of flat tori with two conical points and elliptic hypergeometric functions, arXiv:1605.02356 [math.AG], May 08 2016, http://arxiv.org/abs/1605.02356
Keiji Matsumoto, The monodromy representations of local systems associated with Lauricella's \(F_D\), arXiv:1604.06226 [math.AG], April 21 2016, http://arxiv.org/abs/1604.06226
Irene Pasquinelli, Deligne-Mostow lattices with three fold symmetry and cone metrics on the sphere, arXiv:1509.05320 [math.GT], September 17 2015, http://arxiv.org/abs/1509.05320
Pasquinelli, Irene. “Deligne-Mostow Lattices with Three Fold Symmetry and Cone Metrics on the Sphere.” arXiv:1509.05320 [math], September 17, 2015. http://arxiv.org/abs/1509.05320.