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

2006/04/19 by de Bobadilla, J. Fernandez, Luengo, I., Melle-Hernandez, A. +1 · 3 citations
#14J17 #32S25 #32S45 #57M25 #57M27 #57R57 Secondary. 14E15 #Algebraic Geometry (math.AG) #FOS: Mathematics #Primary. 14B05

paper · doi:10.48550/arxiv.math/0604420

Abstract

It is a very old and interesting open problem to characterize those collections of embedded topological types of local plane curve singularities which 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 unique singularity which is locally irreducible (i.e. C is unicuspidal) with one Puiseux pair.

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