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.
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Artal Bartolo, E., Gorrochategui, L., Luengo, I., & Melle-Hernández, A. (2017). On some conjectures about free and nearly free divisors. In Singularities and Computer Algebra: Festschrift for Gert-Martin Greuel on the Occasion of his 70th Birthday (pp. 1–19). Springer International Publishing. https://doi.org/10.1007/978-3-319-28829-1_1
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