QUASI-PROJECTIVITY, ARTIN-TITS GROUPS, AND PENCIL MAPS

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 niteness properties of such groups and exhibit examples of hyperplane complements whose fundamental groups satisfy Fk 1 but not Fk for any k.