Abstract
In this paper, we study numerical properties of Chern classes of certain covering manifolds. One of the main results is the following: Let ψ : X → P n 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 c i ( X) be the i-th Chern class of X. Then (i) if the canonical divisor K X is numerically effective, then (−1) k c k ( X) ( k ≥ 2) is numerically positive, and (ii) if X is of general type, then (−1) n c i l ( X) ⋯ c i r , ( X) > 0, where i l + … + i r = n. Furthermore we show that the same properties hold for certain Kummer coverings.
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