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

Full-text PDF

Abstract | References | Additional Information

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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Additional Information

**Alexandru Dimca**

Affiliation:
Laboratoire J. A. Dieudonné, UMR du CNRS 6621, Université de Nice–Sophia Antipolis, Parc Valrose, 06108 Nice Cedex 02, France

MR Author ID:
58125

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

MR Author ID:
168600

ORCID:
0000-0002-5060-7754

Email:
a.suciu@neu.edu

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