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Third Mini-Workshop IMAC-SINGACOM in La Plana: Topics in Singularities and Valuations Castellón, September 7-9, 2016 On some conjectures about irreducible free and nearly free divisors A. Melle Hernández1 In this talk families of examples of irreducible plane curves which are free and nearly free curves in the complex projective plane which are not rational curves and whose local singularities can have an arbitrary number of branches are given. All these examples answer negatively to some conjectures proposed by A. Dimca and G. Sticlaru. Our examples say nothing about the most remarkable conjecture by A. Dimca and G. Sticlaru, i.e. every rational cuspidal plane curve is either free or nearly free. This is a joint work with E. Artal, L. Gorrochategui and I. Luengo. 1 ICMAT & Departamento de Álgebra Facultad de Matemáticas, Universidad Complutense de Madrid 28040, Madrid, España. [email protected]
