Topological invariance of intersection lattices of arrangements in $\mathbf{CP}^2$

Let ${\mathcal{A}^{\ast}} = \{ {l_{1}},{l_{2}},...,{l_n}\}$ be a line arrangement in $\mathbb{C}{\mathbb{P}^2}$, i.e., a collection of distinct lines in $\mathbb{C}{\mathbb{P}^2}$. Let $L({\mathcal{A}^{\ast}})$ be the set of all intersections of elements of ${A^{\ast}}$ partially ordered by $X \leq Y \Leftrightarrow Y \subseteq X$. Let $M({\mathcal{A}^{\ast}})$ be $\mathbb{C}{\mathbb{P}^2} - \cup {\mathcal{A}^{\ast}}$ where $\cup {\mathcal{A}^{\ast}} = \cup \{ {l_i}:1 \leq i \leq n\}$. The central problem of the theory of arrangement of lines in $\mathbb{C}{\mathbb{P}^2}$ is the relationship between $M({\mathcal{A}^{\ast}})$ and $L({\mathcal{A}^{\ast}}).$