  In this paper we introduce a formula to compute Chern classes of fibered
products of algebraic surfaces. For f, a generic projection to CP^2, of an
algebraic surface X, we define X_k (for k smaller than degf) to be the k
products of X over f minus the big diagonal. For k=degf, X_k is called the
Galois cover of f w.r.t. full symmetric group. Let S be the branch curve of f.
We give a formula for c_1^2 and c_2 of X_k, in terms of degf, degS, and the
number of cusps, nodes and branch points of S. We apply the formula in 2
examples and add a conjecture concerning the spin structure of fibered products
of Veronese surfaces.
