Makoto Namba(Otemon Gakuin Univ.)

Title : Galois coverings of the complex projective line and related differential equations

Abstract :

For a given finite group G, there exists a Galois covering (X,f) of the complex projective line with the covering transformation group G, whose number 's' of branch points depends on the presentation of G. Let (Y,g) be the universal covering of X. In this lecture, we look for simultaneous differentail equations which describe the inverse map of fg. (For s = 3, the Gauss' hypergeometric differential equation is known to be such an equation.)