Computing the Braid Monodromy of Completely Reducible n -gonal Curves

Braid monodromy is an important tool for computing invariants of curves and surfaces. In this paper, the rectangular braid diagram (RBD) method is proposed to compute the braid monodromy of a completely reducible n-gonal curve, i.e., the curves in the form (y−y1(x))…(y−yn(x))e0, where n∈ Z+ and yi∈ C[x]. Also, an algorithm is presented to compute the Alexander polynomial of these curve complements using Burau representations of braid groups. Examples for each computation are provided.