Topological invariance of intersection lattices of arrangements in CP^2

Abstract

Let $\scr A^*=\{l_1,l_2,\cdots,l_n\}$ be a line arrangement in ${\mathbb{CP}}^2$, i.e., a collection of distinct lines in ${\mathbb{CP}}^2$. Let $L(\scr A^*)$ be the set of all intersections of elements of $A^{\ast }$ partially ordered by $X\le Y\iff Y\subseteq X$. Let $M(\scr A^*)$ be $\Bbb{CP}^2-\bigcup\scr A^*$ where $\bigcup\scr A^*= \bigcup\{l_i\colon\ 1\leq i\leq n\}$. The central problem of the theory of arrangement of lines in ${\mathbb{CP}}^2$ is the relationship between $M(\scr A^*)$ and $L(\scr A^*)$.

arXiv comment6 pages

Cited by in corpus (4)

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• The boundary manifold of a complex line arrangement
• Fundamental groups of real arrangements and torsion in the lower central series quotients