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...

ver descrição completa

Detalhes bibliográficos
Autores: Fernández de Bobadilla de Olarzábal, Javier José, Luengo Velasco, Ignacio, Melle Hernández, Alejandro, Némethi, A.
Formato: capítulo de livro
Fecha de publicación:2007
País:España
Recursos:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/53145
Acesso em linha:https://hdl.handle.net/20.500.14352/53145
Access Level:acceso abierto
Palavra-chave: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
id ES_d8eee4eaa92daf1ede4b01086cd223e5
oai_identifier_str oai:docta.ucm.es:20.500.14352/53145
network_acronym_str ES
network_name_str España
repository_id_str
spelling On rational cuspidal plane curves, open surfaces and local singularitiesFernández de Bobadilla de Olarzábal, Javier JoséLuengo Velasco, IgnacioMelle Hernández, AlejandroNémethi, A.514Cuspidal rational plane curveslogarithmic Kodaira dimensionNagata-Coolidge problemFlenner-Zaidenberg rigidity conjecturesurface singularitiesQ-homology spheresSeiberg-Witten invariantgraded rootsHeegaard Floer homologyOzsváth-Szabó invariants.Geometría1204 GeometríaLet 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.World Scientific Publishing Co.Cheniot, D.Dutertre, D.Murolo, C.Trotman, D.Pichon, A.Universidad Complutense de Madrid20072007-01-0120072007-01-01book parthttp://purl.org/coar/resource_type/c_3248info:eu-repo/semantics/bookPartapplication/pdfhttps://hdl.handle.net/20.500.14352/53145reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/531452026-06-02T12:44:21Z
dc.title.none.fl_str_mv On rational cuspidal plane curves, open surfaces and local singularities
title On rational cuspidal plane curves, open surfaces and local singularities
spellingShingle On rational cuspidal plane curves, open surfaces and local singularities
Fernández de Bobadilla de Olarzábal, Javier José
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
title_short On rational cuspidal plane curves, open surfaces and local singularities
title_full On rational cuspidal plane curves, open surfaces and local singularities
title_fullStr On rational cuspidal plane curves, open surfaces and local singularities
title_full_unstemmed On rational cuspidal plane curves, open surfaces and local singularities
title_sort On rational cuspidal plane curves, open surfaces and local singularities
dc.creator.none.fl_str_mv Fernández de Bobadilla de Olarzábal, Javier José
Luengo Velasco, Ignacio
Melle Hernández, Alejandro
Némethi, A.
author Fernández de Bobadilla de Olarzábal, Javier José
author_facet Fernández de Bobadilla de Olarzábal, Javier José
Luengo Velasco, Ignacio
Melle Hernández, Alejandro
Némethi, A.
author_role author
author2 Luengo Velasco, Ignacio
Melle Hernández, Alejandro
Némethi, A.
author2_role author
author
author
dc.contributor.none.fl_str_mv Cheniot, D.
Dutertre, D.
Murolo, C.
Trotman, D.
Pichon, A.
Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 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
topic 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
description 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.
publishDate 2007
dc.date.none.fl_str_mv 2007
2007-01-01
2007
2007-01-01
dc.type.none.fl_str_mv book part
http://purl.org/coar/resource_type/c_3248
dc.type.openaire.fl_str_mv info:eu-repo/semantics/bookPart
format bookPart
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/53145
url https://hdl.handle.net/20.500.14352/53145
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv World Scientific Publishing Co.
publisher.none.fl_str_mv World Scientific Publishing Co.
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869421244947890176
score 15,301603

Registos relacionados