LA-MOKA: A Combinatorial Discretization Algorithm for the Braid Monodromy of Line Arrangements

Computing braid monodromy is a key tool for studying the topology of algebraic curves in the complex projective plane $\mathbb{P}^2$. We present an algorithm, named LA-MOKA, to compute this invariant in the specific case of complex line arrangements. To safely manage the problem of floating-point approximations when working over number fields, we translate the continuous geometry into a discrete combinatorial structure. We establish explicit conditions on this discretization that guarantee the topological correctness of the computed braid monodromy.