On algebraic surfaces associated to line arrangements

Autor:	Wang, Zhenjian
Rok vydání:	2016
Předmět:	Mathematics - Algebraic Geometry Primary 32S22 Secondary 14J17 14J70 32S25
Druh dokumentu:	Working Paper
Popis:	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. Comment: 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
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1612.06730 Zobrazit plný text záznamu View this record from Arxiv