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On Some Conjectures About Free and Nearly Free Divisors

In: Singularities and Computer Algebra

Author

Listed:
  • Enrique Artal Bartolo

    (Universidad de Zaragoza, IUMA, Departamento de Matemáticas, Facultad de Ciencias)

  • Leire Gorrochategui

    (Universidad Complutense, Departamento de Álgebra, Facultad de Ciencias Matemáticas)

  • Ignacio Luengo

    (Universidad Complutense, ICMAT (CSIC-UAM-UC3M-UCM), Departamento de Álgebra, Facultad de Ciencias Matemáticas)

  • Alejandro Melle-Hernández

    (Universidad Complutense, ICMAT (CSIC-UAM-UC3M-UCM), Departamento de Álgebra, Facultad de Ciencias Matemáticas)

Abstract

In this paper we provide infinite families of non-rational irreducible free divisors or nearly free divisors in the complex projective plane. Moreover, their corresponding local singularities can have an arbitrary number of branches. All these examples contradict some of the conjectures proposed by Dimca and Sticlaru. Our examples say nothing about the most remarkable conjecture by A. Dimca and G. Sticlaru, which predicts that every rational cuspidal plane curve is either free or nearly free.

Suggested Citation

  • Enrique Artal Bartolo & Leire Gorrochategui & Ignacio Luengo & Alejandro Melle-Hernández, 2017. "On Some Conjectures About Free and Nearly Free Divisors," Springer Books, in: Wolfram Decker & Gerhard Pfister & Mathias Schulze (ed.), Singularities and Computer Algebra, pages 1-19, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-28829-1_1
    DOI: 10.1007/978-3-319-28829-1_1
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