  For a line arrangement in the complex projective plane $\mathbb{P}^2$, we
investigate the compactification $\overline{F}$ of the affine Milnor fiber in
$\mathbb{P}^3$ and its minimal resolution $\widetilde{F}$. We compute the Chern
numbers in terms of the combinatorics of the line arrangement, then we show
that the minimal resolution is never a quotient of a ball; in addition, we also
prove that $\widetilde{F}$ is of general type when the arrangement has only
nodes or triple points as singularities.
