Combinatorial and geometric invariants of configuration spaces

Let $V$ be a finite dimensional vector space over a field $\mathbb{K}$. A \emph{subspace arrangement} $\mathcal{A}$ in $V$ is a (finite) family of (affine) subspaces of $V$. The \emph{combinatorial data} of a subspace arrangement are encoded by the \emph{intersection lattice} $L(\mathcal{A})$ which is the poset of all the intersections between the elements of $\mathcal{A}$ ordered by reversing inclusion, that is $X\leq Y$ iff $X\supseteq Y$. \emph{The complement of a subspace arrangement} is $\mathcal{M}(\mathcal{A}):=V\setminus \bigcup_{H\in\mathcal{A}} H$ and, in the theory of subspace arrangements, one of the main problems is to determine which topological properties of $\mathcal{M}(\mathcal{A})$ (or of some spaces derived from $\mathcal{M}(\mathcal{A})$) are combinatorially determined, that is which properties depend only on the intersection lattice. In this thesis we deal with problems of this kind associated to De Concini-Procesi wonderful models of subspace arrangements and to Milnor fibre of a hyperplane arrangement.