On rational cuspidal plane curves, open surfaces and local singularities
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, whet...
| Autores: | , , , |
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| Tipo de recurso: | capítulo de libro |
| Fecha de publicación: | 2007 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/53145 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/53145 |
| Access Level: | acceso abierto |
| Palabra clave: | 514 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. Geometría 1204 Geometría |
| Sumario: | 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. |
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