Abstract

In this paper we study generic coverings of $\mathbb{C}^2$ branched over a curve s.t. the total space is a normal analytic surface, in terms of a graph representing the monodromy of the covering, called monodromy graph. A complete description of the monodromy graphs and of the local fundamental groups is found in case the branch curve is $\lbrace x^n=y^m\rbrace $ and the degree of the cover is equal to $n$ or $n-1$