On the integral Seifert form of plane curve germs with two branches. (Q1408211)

Let \(f: (\mathbb{C}^2 , 0)\to(\mathbb{C}, 0)\) be a plane curve germ with an isolated singularity. Then it is known [\textit{E. Robin}, C. R. Acad. Sci., Paris, Sér. I, Math. 329, No. 10, 863--866 (1999; Zbl 0945.32017)] that (under certain conditions) 2 such plane curve germs, with 2 branches, are isometric provided they have isomorphic integral Seifert form. In this note, a converse of that result is established, without any conditions. The proof uses the weight filtration on the integral homology of the Milnor fibre. Also it is pointed out that such a result does not hold for 3-branch germs.