# Tesi etd-07152015-121132

Thesis type
Tesi di dottorato di ricerca
Author
SERVENTI, MATTEO
URN
etd-07152015-121132
Title
Combinatorial and geometric invariants of configuration spaces
Settore scientifico disciplinare
MAT/03
Corso di studi
SCIENZE DI BASE
Commissione
tutor Prof. Salvetti, Mario
Parole chiave
• hyperplane arrangements
• De Concini-Procesi wonderful models
• Milnor fibre
Data inizio appello
12/08/2015;
Consultabilità
completa
Riassunto analitico
Let $V$ be a finite dimensional vector space over a field $\mathbb{K}$. A \emph{subspace arrangement} $\mathcal{A}$ in $V$ is a (finite)<br>family of (affine) subspaces of $V$. The \emph{combinatorial data} of a subspace arrangement are encoded by the<br>\emph{intersection lattice} $L(\mathcal{A})$ which is the poset of all the intersections between the elements of $\mathcal{A}$ ordered by<br>reversing inclusion, that is $X\leq Y$ iff $X\supseteq Y$.<br><br>\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<br>subspace arrangements, one of the main problems is to determine which topological properties of $\mathcal{M}(\mathcal{A})$ (or of some<br>spaces derived from $\mathcal{M}(\mathcal{A})$) are<br>combinatorially determined, that is which properties depend only on the intersection lattice.<br>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.
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