  In this manuscript we prove that if two cuspidal plane curves have equivalent
braid monodromy factorizations, then they are smoothly isotopic in the plane.
As a consequence of this and the Chisini conjecture, we obtain that if two
discriminant curves (or branch curves in other terminology) of generic
projections (to the plane) of surfaces of general type imbedded in a projective
space by means of a multiple canonical class have equivalent braid monodromy
factorizations, then the surfaces are diffeomorphic (if we consider them as
real 4-folds).
