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

1998/12/07 by Michael Kapovich, John J. Millson · 3 citations
Mathematics · #Advanced Algebra and Geometry #Affine transformation #Affine variety #Algebra over a field #Algebraic Geometry and Number Theory #Algebraic group #Algebraic number #Algebraic variety #Finitely-generated abelian group #Group (periodic table) #Homotopy and Cohomology in Algebraic Topology #Mathematical analysis #Mathematics #Projective test #Pure mathematics #Variety (cybernetics)

paper · doi:10.1007/bf02701766

openalex publication_date 1998/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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 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.

Citations

• Artin-Gruppen und Coxeter-Gruppen
• Infinitesimal computations in topology
• CRITICAL POINTS OF SMOOTH FUNCTIONS AND THEIR NORMAL FORMS
• Die Fundamentalgruppe des Raumes der regul�ren Orbits einer endlichen komplexen Spiegelungsgruppe
• Théorie de Hodge : III
• Théorie de Hodge : II
• Fundamental Groups of Compact Kähler Manifolds
• Real homotopy theory of K�hler manifolds

Cited by

• Deformations of representations of fundamental groups of complex varieties
• Fundamental groups of links of isolated singularities
• Michael Kapovich [wikipedia]