BRANCHED-COVERINGS OF SURFACES WITH AMPLE COTANGENT BUNDLE

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) --> (u(n) , v(m)). We characterize ampleness of T* X. A class of examples of such X, which are branched covers of degree two, is provided.