Quasi-Kähler Bestvina-Brady groups

Details Quasi-Kähler Bestvina-Brady groups Quasi-Kähler Bestvina-Brady groups

2006-03-18

arxiv.org/abs/math/0603446v3

Journal of Algebraic Geometry 17 (2008), no. 1, 185-197

Mathematics

Algebraic Geometry

11 pages, accepted for publication by the Journal of Algebraic Geometry

Scientific paper

10.1090/S1056-3911-07-00463-8

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.

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