Abstract.
To a plane algebraic curve of degree n, Moishezon associated a braid monodromy homomorphism from a finitely generated free group to Artin's braid group Bn. Using Hansen's polynomial covering space theory, we give a new interpretation of this construction. Next, we provide an explicit description of the braid monodromy of an arrangement of complex affine hyperplanes, by means of an associated "braided wiring diagram". The ensuing presentation of the fundamental group of the complement is shown to be Tietze-I equivalent to the Randell-Arvola presentation. Work of Libgober then implies that the complement of a line arrangement is homotopy equivalent to the 2-complex modeled on either of these presentations. Finally, we prove that the braid monodromy of a line arrangement determines the intersection lattice. Examples of Falk then show that the braid monodromy carries more information than the group of the complement, thereby answering a question of Libgober.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: September 9, 1996
Rights and permissions
About this article
Cite this article
Cohen, D., Suciu, A. The braid monodromy of plane algebraic curves and hyperplane arrangements. Comment. Math. Helv. 72, 285–315 (1997). https://doi.org/10.1007/s000140050017
Published:
Issue Date:
DOI: https://doi.org/10.1007/s000140050017