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On rational cuspidal plane curves, open surfaces and local singularities


Fernández de Bobadilla de Olarzábal, Javier José and Luengo Velasco, Ignacio and Melle Hernández, Alejandro and Némethi , A. (2007) On rational cuspidal plane curves, open surfaces and local singularities. In Singularity theory. World Scientific Publishing Co. , Singapore, pp. 411-442. ISBN 978-981-270-410-8

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Let 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.

Item Type:Book Section
Additional Information:

Conference: Marseille Singularity School and Conference Location: CIRM, Luminy, France Date: Jan 24-Feb 25, 2005

Uncontrolled Keywords:Cuspidal rational plane curves, logarithmic Kodaira dimension, Nagata-Coolidge problem, Flenner-Zaidenberg rigidity conjecture, surface singularities, Q-homology spheres, Seiberg-Witten invariant, graded roots, Heegaard Floer homology, Ozsváth-Szabó invariants.
Subjects:Sciences > Mathematics > Geometry
ID Code:16567

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