Quasi-K\"ahler Bestvina-Brady groups
Algebraic Geometry
2007-12-04 v3 Group Theory
Abstract
A finite simple graph \G determines a right-angled Artin group G_\G, 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_\G is the kernel of the projection G_\G \to \Z, which sends each generator v to 1. We establish precisely which graphs \G give rise to quasi-K\"ahler (respectively, K\"ahler) groups N_\G. 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.
Cite
@article{arxiv.math/0603446,
title = {Quasi-K\"ahler Bestvina-Brady groups},
author = {Alexandru Dimca and Stefan Papadima and Alexander I. Suciu},
journal= {arXiv preprint arXiv:math/0603446},
year = {2007}
}
Comments
11 pages, accepted for publication by the Journal of Algebraic Geometry