Fernández de Bobadilla de Olarzábal, Javier JoséLuengo Velasco, IgnacioMelle Hernández, AlejandroNémethi, A.Cheniot, D.Dutertre, D.Murolo, C.Trotman, D.Pichon, A.2023-06-202023-06-202007978-981-270-410-8https://hdl.handle.net/20.500.14352/53145Conference: Marseille Singularity School and Conference Location: CIRM, Luminy, France Date: Jan 24-Feb 25, 2005Let C be an irreducible projective plane curve in the complex projective space P(2). The classification of such curves, up to the action of the automorphism group PGL(3, C) on P(2), is a very difficult open problem with many interesting connections. The main goal is to determine, for a given d, whether there exists a projective plane curve of degree d having a fixed number of singularities of given topological type. In this note we are mainly interested in the case when C is a rational curve. The aim of this article is to present some of the old conjectures and related problems, and to complete them with some results and new conjectures from the recent work of the authors.engbook parthttp://www.worldscientific.com/doi/abs/10.1142/9789812707499_0015http://www.worldscientific.com/open access514Cuspidal rational plane curveslogarithmic Kodaira dimensionNagata-Coolidge problemFlenner-Zaidenberg rigidity conjecturesurface singularitiesQ-homology spheresSeiberg-Witten invariantgraded rootsHeegaard Floer homologyOzsváth-Szabó invariants.Geometría1204 Geometría