Discriminant of a Germ Φ: (C2 , 0)→(C2 , 0) and Seifert Fibred Manifolds

Abstract

Let f and g be two analytic function germs without common branches. We define the Jacobian quotients of (g, f), which are ‘first order invariants’ of the discriminant curve of (g, f), and we prove that they only depend on the topological type of (g, f). We compute them with the help of the topology of (g, f). If g is a linear form transverse to f, the Jacobian quotients are exactly the polar quotients of f and we affirm the results of D. T. Lê, F. Michel and C. Weber.