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For a line arrangement
in the complex projective plane
, we investigate the compactification
of the affine Milnor fiber
and its minimal resolution
. We compute the Chern numbers of
in terms of the combinatorics of the line arrangement
. As applications of the computation of the Chern numbers, we show that the minimal resolution is never a quotient of a ball; in addition, we also prove that
is of general type when the arrangement has only nodes or triple points as singularities. Finally, we compute all the Hodge numbers of some
by using some knowledge about the Milnor fiber monodromy of the arrangement.