Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Quasi-Kähler Bestvina-Brady groups


Authors: Alexandru Dimca, Stefan Papadima and Alexander I. Suciu
Journal: J. Algebraic Geom. 17 (2008), 185-197
DOI: https://doi.org/10.1090/S1056-3911-07-00463-8
Published electronically: June 27, 2007
MathSciNet review: 2357684
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Abstract: A finite simple graph $ \Gamma$ determines a right-angled Artin group $ G_\Gamma$, with one generator for each vertex $ v$, and with one commutator relation $ vw=wv$ for each pair of vertices joined by an edge. The Bestvina-Brady group $ N_\Gamma$ is the kernel of the projection $ G_\Gamma\to \mathbb{Z}$, which sends each generator $ v$ to $ 1$. We establish precisely which graphs $ \Gamma$ give rise to quasi-Kähler (respectively, Kähler) groups $ N_\Gamma$. This yields examples of quasi-projective groups which are not commensurable (up to finite kernels) to the fundamental group of any aspherical, quasi-projective variety.


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Alexandru Dimca
Affiliation: Laboratoire J. A. Dieudonné, UMR du CNRS 6621, Université de Nice–Sophia Antipolis, Parc Valrose, 06108 Nice Cedex 02, France
Email: dimca@math.unice.fr

Stefan Papadima
Affiliation: Instititue of Mathematics Simion Stoilow, Romanian Academy, P.O. Box 1-764, RO-014700 Bucharest, Romania
Email: Stefan.Papadima@imar.ro

Alexander I. Suciu
Affiliation: Department of Mathematics, Northeastern University, Boston, Massachusetts 02115
Email: a.suciu@neu.edu

DOI: https://doi.org/10.1090/S1056-3911-07-00463-8
Received by editor(s): March 22, 2006
Received by editor(s) in revised form: July 28, 2006
Published electronically: June 27, 2007
Additional Notes: The second author was partially supported by CERES grant 4-147/12.11.2004 of the Romanian Ministry of Education and Research. The third author was partially supported by NSF grant DMS-0311142