A generalized Desargues configuration and the pure braid group

Raul Cordovil, António Guedes de Oliveira, Michel Las Vergnas
1996 Discrete Mathematics  
In this paper, a configuration with n = (g) points in the plane is described. This configuration, as a matroid, is a Desargues configuration if d = 5, and the union of (~) such configurations if d > 5. As an oriented matroid, it is a rank 3 truncation of the directed complete graph on d vertices. From this fact, it follows from a version of the Lefschetz Zariski theorem implied by results of Salvetti that the fundamental group ~ of the complexification of its line arrangement is Artin's pure
more » ... coloured) braid group on d strands. In this paper we obtain, by using techniques introduced by Salvetti, a new algorithm for finding a presentation of ~ based on this particular configuration.
doi:10.1016/0012-365x(95)00152-m fatcat:li33gjt3rnaj3msebhh3twsng4