Geodesic
On Algebraic Surfaces Associated with Line Arrangements
Canadian journal of mathematics, Tome 71 (2019) no. 2, pp. 471-499

Voir la notice de l'article provenant de la source Cambridge University Press

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 $\tilde{F}$. We compute the Chern numbers of $\tilde{F}$ 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 $\tilde{F}$ is of general type when the arrangement has only nodes or triple points as singularities. Finally, we compute all the Hodge numbers of some $\tilde{F}$ by using some knowledge about the Milnor fiber monodromy of the arrangement.
DOI : 10.4153/CJM-2017-052-3
Mots-clés : line arrangement, Milnor fiber, algebraic surface, Chern number 
Wang, Zhenjian. On Algebraic Surfaces Associated with Line Arrangements. Canadian journal of mathematics, Tome 71 (2019) no. 2, pp. 471-499. doi: 10.4153/CJM-2017-052-3
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