Numerical properties of Chern classes of certain covering manifolds

AbstractIn this paper, we study numerical properties of Chern classes of certain covering manifolds. One of the main results is the following: Let ψ : X → Pn be a finite covering of the n-dimensional complex projective space branched along a hypersurface with only simple normal crossings and suppose X is nonsingular. Let ci(X) be the i-th Chern class of X. Then (i) if the canonical divisor KX is numerically effective, then (−1)kck(X) (k ≥ 2) is numerically positive, and (ii) if X is of general type, then (−1)ncil (X) ⋯ cir, (X) > 0, where il + … + ir = n. Furthermore we show that the same properties hold for certain Kummer coverings