Let f : X → Y be a branched
covering of compact complex surfaces, where the ramification set in X consists of
smooth curves meeting with at most normal crossings and Y has ample cotangent
bundle. We further assume that f is locally of form (u,v) → (un,vm). We
characterize ampleness of T∗X. A class of examples of such X, which are branched
covers of degree two, is provided.