“…On the other hand, the generic braid monodromy of a plane projective curve is a powerful invariant that provides a way to compute the fundamental group of its complement, and it was originally described as a formalization of the Zariski-van Kampen method [42,26] (see [35,23]; also [18] and references therein for a detailed exposition on the subject). However, generic braid monodromies are much more powerful invariants, since in fact they encode the topology of the embedding of the curve, as well as the isomorphism problem for surfaces whose branching locus over P 2 is a given curve (see [13,29,37,15,14,28,9,21,1], to name only a few).…”