Curves of minimal degree with prescribed planar singularities

In this paper we study the existence of reduced and irreducible complex or real projective curves contained in an ambient normal projective variety wi th prescribed singularities and with "low degree". We consider germs of pla nar singularities of curves, up to topological or equisingular equivalence. The main result is an existence theorem for plane curves with ordinary sin gularities which improves previous results by Greuel, Lessen and Shustin.