On algebraic surfaces associated to line arrangements

Zhenjian Wang

On algebraic surfaces associated to line arrangements

Algebraic Geometry 2017-02-03 v2

Authors: Zhenjian Wang

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.

Keywords

affine algebraic geometry incidence geometry of points and lines minimal surfaces

Cite

@article{arxiv.1612.06730,
  title  = {On algebraic surfaces associated to line arrangements},
  author = {Zhenjian Wang},
  journal= {arXiv preprint arXiv:1612.06730},
  year   = {2017}
}

Comments

29 pages. We compute the Chern numbers and prove that the surfaces are not ball quotients, some surfaces are of general type. Some details of the computations are removed and more examples are added

On algebraic surfaces associated to line arrangements

Abstract

Keywords

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