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# On algebraic surfaces associated with line arrangements

For a line arrangement $\mathcal{A}$ in the complex projective plane $\mathbb{P}^2$, we investigate the compactification $\overline{F}$ in $\mathbb{P}^3$ of the affine Milnor fiber $F$ and its minimal resolution $\widetilde{F}$. We compute the Chern numbers of $\widetilde{F}$ in terms of the combinatorics of the line arrangement $\mathcal{A}$. 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 $\widetilde{F}$ is of general type when the arrangement has only nodes or triple points as singularities; finally, we compute all the Hodge numbers of some $\widetilde{F}$ by using some knowledge about the Milnor fiber monodromy of the arrangement.