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

  • Michael Kapovich
  • John J. Millson


We prove that for any affine variety S defined overQ 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 X(G, PO(3)) = 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.


Fundamental Group Representation Variety Artin Group Abstract Arrangement Zariski Open Subset 
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Copyright information

© Publications mathématiques de l’I.H.É.S 1998

Authors and Affiliations

  • Michael Kapovich
    • 1
  • John J. Millson
    • 2
  1. 1.Department of MathematicsUniversity of UtahSalt Lake CityUSA
  2. 2.Department of MathematicsUniversity of MarylandCollege ParkUSA

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