Computing the Braid Monodromy of Completely Reducible n-gonal Curves

Mehmet Emin Aktas, Esra Akbas

Abstract: 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))=0, 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.