Braid monodromy of some Brieskorn-pham singularities

For germs of isolated hypersurface singularities Lyashko and Looijenga introduced a map LL on the complement of the bifurcation set. It takes values in the space of simple polynomials of degree equal to the Milnor number μ of the singularity, and thus induces a map LL* from the fundamental group to the braid group on μ strands. For the case of curve singularities given by a polynomial x3 + yℓ+1 we give a uniform description of the image LL* and derive a presentation of the discriminant knot group, i.e. for the fundamental group of the complement to the discriminant divisor.