On Some Conjectures About Free and Nearly Free Divisors

Enrique Artal Bartolo (), Leire Gorrochategui (), Ignacio Luengo () and Alejandro Melle-Hernández ()
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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

A chapter in Singularities and Computer Algebra, 2017, pp 1-19 from Springer

Abstract: 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.

Keywords: Free divisors; Nearly free curves; 14A05; 14R15 (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-28829-1_1

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DOI: 10.1007/978-3-319-28829-1_1

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