The Braid Monodromy of Plane Algebraic Curves and Hyperplane Arrangements

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dc.creatorCohen, Daniel C.
dc.creatorSuciu, Alexander I.
dc.date1996-08-02
dc.date.accessioned2026-07-07T09:06:54Z
dc.date.available2026-07-07T09:06:54Z
dc.descriptionTo a plane algebraic curve of degree n, Moishezon associated a braid monodromy homomorphism from a finitely generated free group to Artin's braid group B_n. 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.
dc.description27 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-graphs
dc.identifierhttps://arxiv.org/abs/alg-geom/9608001
dc.identifierhttp://arxiv.org/abs/alg-geom/9608001
dc.identifierCommentarii Mathematici Helvetici 72 (1997), no. 2, 285-315.
dc.identifierdoi:10.1007/s000140050017
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/150181
dc.subjectAlgebraic Geometry
dc.subject14H30, 20F36, 52B30 (Primary); 05B35, 32S25, 57M05 (Secondary)
dc.titleThe Braid Monodromy of Plane Algebraic Curves and Hyperplane Arrangements
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