Topological type of discriminants of some special families. (English) Zbl 1524.14079
Summary: We will describe the topological type of the discriminant curve of the morphism \((\ell, f)\), where \(\ell\) is a smooth curve and \(f\) is an irreducible curve (branch) of multiplicity less than five or a branch such that the difference between its Milnor number and Tjurina number is less than 3. We prove that for a branch of these families, the topological type of the discriminant curve is determined by the semigroup, the Zariski invariant and at most two other analytical invariants of the branch.
MSC:
| 14J17 | Singularities of surfaces or higher-dimensional varieties |
| 32S15 | Equisingularity (topological and analytic) |
Keywords:
discriminant curve; nondegenerate singularity; Newton polygon; Zariski invariant; Milnor number; Tjurina numberReferences:
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