Local Transformations with Fixed Points on Complex Spaces with Singularities.

with coefficients which are analytic in S. This defines for us a topological space which will be denoted by U. If R is any subset of S then U(R) will denote those points of U whose base points are in R. Now there is a function D(z) analytic and not identically zero in S such that for E denoting the points of S where D vanishes the subset U(E) are possible singularities on U. However, U U(E) = U(S E) shall be a complex analytic coordinate space. If m, is the degree of 4, in the variable r, and if m = ml ... mn then the system (1) has m sets of solutions