Topological type of discriminants of some special families

Abstract We will describe the topological type of discriminant curve morphism $$(\ell , f)$$ ( ℓ , f ) where $$\ell $$ is a smooth and f an irreducible (branch) multiplicity less than five or branch such that difference between its Milnor number Tjurina 3. prove for these families, determined by semigroup, Zariski invariant at most two other analytical invariants branch.