Classification of rational unicuspidal projective curves whose singularities have one Puiseux pair

摘要

It is a very old and interesting open problem to characterize thosecollections of embedded topological types of local plane curve singularitieswhich may appear as singularities of a projective plane curve C of degree d.The goal of the present article is to give a complete (topological)classification of those cases when C is rational and it has a uniquesingularity which is locally irreducible (i.e. C is unicuspidal) with onePuiseux pair.