On algebraic representatives of homeomorphism types of analytic hypersurface germs

A question of B. Teissier, inspired by a previous problem of R. Thom, asks whether for any germ of complex analytic hypersurface there exists a germ of complex algebraic hypersurface with the same topological type. Up to now only the case of germs with an isolated singularity is kwown. In this article we answer in the affirmative the case 1-dimensional singular set, also for embedded topological types.