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On Algebraic Surfaces Associated with Line Arrangements

  • Zhenjian Wang (a1)

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.

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Canadian Journal of Mathematics
  • ISSN: 0008-414X
  • EISSN: 1496-4279
  • URL: /core/journals/canadian-journal-of-mathematics
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