On Sextic Curves with Big Milnor Number

  • Enrique Artal Bartolo
  • Jorge Carmona Ruber
  • José Ignacio Cogolludo Agustín
Part of the Trends in Mathematics book series (TM)


In this work we present an exhaustive description, up to projective isomorphism, of all irreducible sextic curves in ℙ2 having a singular point of type ,\( \mathbb{A}_n ,n \geqslant 15 \) n ≥ 15, only rational singularities and global Milnor number at least 18. Moreover, we develop a method for an explicit construction of sextic curves with at least eight — possibly infinitely near — double points. This method allows us to express such sextic curves in terms of arrangements of curves with lower degrees and it provides a geometric picture of possible deformations. Because of the large number of cases, we have chosen to carry out only a few to give some insights into the general situation.

2000 Mathematics Subject Classification

Primary 14HlO, 14H30, 14D06j Secondary 14Q05, 32S20, 32S50, 14H52 

Key words and phrases

Equisingular family sextic curves deformation fundamental group 


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Copyright information

© Springer Basel AG 2002

Authors and Affiliations

  • Enrique Artal Bartolo
    • 1
  • Jorge Carmona Ruber
    • 2
  • José Ignacio Cogolludo Agustín
    • 3
  1. 1.Departamento de MatemáticasUniversidad de ZaragozaZaragozaSpain
  2. 2.Departamento de Sistemas informáticos y programaciónUniversidad ComplutenseMadridSpain
  3. 3.Departamento de ÁlgebraUniversidad ComplutenseMadridSpain

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