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

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

2010-05-28

arxiv.org/abs/1005.5225v1

Mathematics

Algebraic Geometry

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

Scientific paper

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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