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arXiv · 1612.06730

On algebraic surfaces associated to line arrangements

Zhenjian Wang
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Abstract

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.

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Zhenjian Wang. 2016-12-20. On algebraic surfaces associated to line arrangements. https://arxiv.org/abs/1612.06730

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