Study on hypergeometric functions

点击翻译按钮获取中文摘要

We succeeded to find a good discretization of the hyperbolic Schwarz map for the Airy equation. This is the starting point of the study of singularities of discrete surfaces. For the hypergeometric differential equation of type (3,6), we found a relation between the two monodromy groups - arithmetic group acting of the domain of type IV, and the maximal non-real finite complex reflection group.We described chambers cut out by six planes in general position in the 3-space.Veronese arrangements of hyperplanes in real projective spaces re studied.A set of generators of the monodromy group of the Appell-Lauricella's hypergeometric equation of type FA is obtained.