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

Michael Kapovich; John Millson

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arXiv · dg-ga/9703007

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

Michael Kapovich·John Millson

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Abstract

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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BibTeX RIS

Michael Kapovich, John Millson. 1997-03-11. On representation varieties of Artin groups, projective arrangements and the fundamental groups of smooth complex algebraic varieties. https://arxiv.org/abs/dg-ga/9703007

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