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

J. Fernandez de Bobadilla; I. Luengo; A. Melle-Hernandez; A. Nemethi

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

J. Fernandez de Bobadilla·I. Luengo·A. Melle-Hernandez·A. Nemethi

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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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J. Fernandez de Bobadilla, I. Luengo, A. Melle-Hernandez, A. Nemethi. 2006-04-19. Classification of rational unicuspidal projective curves whose singularities have one Puiseux pair. https://arxiv.org/abs/math/0604420

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