This week’s recommended algebraic geometry paper is:
Quasi-projectivity, Artin-Tits Groups, and Pencil Maps
Authors: Enrique Artal Bartolo, Jose Ignacio Cogolludo-Agustin, Daniel Matei, arXiv:1005.5225v1
(Submitted on 28 May 2010)
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 $k$.
