# Quasi-projectivity, Artin-Tits Groups, and Pencil Maps

Authors
Type
Preprint
Publication Date
May 28, 2010
Submission Date
May 28, 2010
Source
arXiv
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## Abstract

We consider the problem of deciding if a group is the fundamental group of a smooth connected complex quasi-projective (or projective) variety using Alexander-based invariants. In particular, we solve the problem for large families of Artin-Tits groups. We also study finiteness properties of such groups and exhibit examples of hyperplane complements whose fundamental groups satisfy $\text{F}_{k-1}$ but not $\text{F}_k$ for any $k$.

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