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

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 $k$.

25 pages, 2 figures, to appear at the LIB60BER Conference Proceedings