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Classification of Rational Unicuspidal Projective Curves whose Singularities Have one Puiseux Pair

  • Javier Fernández de Bobadilla
  • Ignacio Luengo
  • Alejandro Melle Hernández
  • Andras Némethi
Conference paper
Part of the Trends in Mathematics book series (TM)

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.

Keywords

Cuspidal rational plane curves logarithmic Kodaira dimension 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2006

Authors and Affiliations

  • Javier Fernández de Bobadilla
    • 1
  • Ignacio Luengo
    • 2
  • Alejandro Melle Hernández
    • 2
  • Andras Némethi
    • 3
    • 4
  1. 1.Department of MathematicsUniversity of UtrechtUtrechtThe Netherlands
  2. 2.Facultad de MatemáticasUniversidad ComplutenseMadridSpain
  3. 3.Department of MathematicsOhio State UniversityColumbusUSA
  4. 4.Rényi Institute of MathematicsBudapestHungary

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