Curves of minimal degree with prescribed planar singularities

Abstract

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