On representation varieties of Artin groups, projective arrangements and the fundamental groups of smooth complex algebraic varieties

Details On representation varieties of Artin groups, projective arrangements and the fundamental groups of smooth complex algebraic varieties On representation varieties of Artin groups, projective arrangements and the fundamental groups of smooth complex algebraic varieties

1997-03-11

arxiv.org/abs/dg-ga/9703007v1

Mathematics

Differential Geometry

68 pages 15 figures

Scientific paper

We prove that for any affine variety S defined over Q there exist Shephard and Artin groups G such that a Zariski open subset U of S is biregular isomorphic to a Zariski open subset of the character variety Hom(G, PO(3))//PO(3). The subset U contains all real points of S . As an application we construct new examples of finitely-presented groups which are not fundamental groups of smooth complex algebraic varieties.

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