Links arising from braid monodromy factorizations

We investigate the local contribution of the braid monodromy factorization in the context of the links obtained by the closure of these braids. We consider plane curves which are arrangements of lines and conics as well as some algebraic surfaces, where some of the former occur as local configurations in degenerated and regenerated surfaces in the latter. In particular, we focus on degenerations which involve intersection points of multiplicity two and three. We demonstrate when the same links arise even when the local arrangements are different.