The braid monodromy of plane algebraic curves and hyperplane arrangements

To a plane algebraic curve of degree n, Moishezon associated a braidmonodromy homomorphism from a finitely generated free group to Artin's braidgroup B_n. Using Hansen's polynomial covering space theory, we give a newinterpretation of this construction. Next, we provide an explicit descriptionof the braid monodromy of an arrangement of complex affine hyperplanes, bymeans of an associated ``braided wiring diagram.'' The ensuing presentation ofthe fundamental group of the complement is shown to be Tietze-I equivalent tothe Randell-Arvola presentation. Work of Libgober then implies that thecomplement of a line arrangement is homotopy equivalent to the 2-complexmodeled on either of these presentations. Finally, we prove that the braidmonodromy of a line arrangement determines the intersection lattice. Examplesof Falk then show that the braid monodromy carries more information than thegroup of the complement, thereby answering a question of Libgober.Comment: 27 pages with 7 figures, author-supplied DVI file available at ftp://ftp.math.neu.edu/Pub/faculty/Suciu_Alex/papers/bmono.dvi AMSTeX v 2.1, pictex, edge-vertex-graph