Fundamental group of plane curves and related invariants

The article under review contains a study of the topology of a pair (P2,C), where C is an algebraic curve in the complex projective plane. The basic problem is to find invariants which are sensitive enough to distinguish many pairs, and for which there is an algorithm for checking this. The homology...

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Detalles Bibliográficos
Autores: Artal Bartolo, Enrique, Carmona Ruber, Jorge, Cogolludo Agustín, José Ignacio, Luengo Velasco, Ignacio, Melle Hernández, Alejandro
Tipo de recurso: capítulo de libro
Fecha de publicación:2000
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/60666
Acceso en línea:https://hdl.handle.net/20.500.14352/60666
Access Level:acceso abierto
Palabra clave:512.772
plane curves
fundamental group
Geometria algebraica
1201.01 Geometría Algebraica
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oai_identifier_str oai:docta.ucm.es:20.500.14352/60666
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spelling Fundamental group of plane curves and related invariantsArtal Bartolo, EnriqueCarmona Ruber, JorgeCogolludo Agustín, José IgnacioLuengo Velasco, IgnacioMelle Hernández, Alejandro512.772plane curvesfundamental groupGeometria algebraica1201.01 Geometría AlgebraicaThe article under review contains a study of the topology of a pair (P2,C), where C is an algebraic curve in the complex projective plane. The basic problem is to find invariants which are sensitive enough to distinguish many pairs, and for which there is an algorithm for checking this. The homology of the complement is certainly computable in this sense, but it is too coarse to be really useful. The fundamental group of the complement, by contrast, is very sensitive. The article reviews the Zariski-van Kampen method for finding a presentation for it. However, it is not clear whether the isomorphism problem for this class of groups is solvable. The article surveys many other invariants, such as the Alexander polynomial and characteristic varieties, which are more computable. This last set of invariants was introduced, in this context, by A. S. Libgober [in Applications of algebraic geometry to coding theory, physics and computation (Eilat, 2001), 215–254, Kluwer Acad. Publ., Dordrecht, 2001Editorial ComplutenseLafuente López, JavierPozo Coronado, Luis MiguelUniversidad Complutense de Madrid20002000-01-0120002000-01-01book parthttp://purl.org/coar/resource_type/c_3248info:eu-repo/semantics/bookPartapplication/pdfhttps://hdl.handle.net/20.500.14352/60666reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/606662026-06-02T12:44:21Z
dc.title.none.fl_str_mv Fundamental group of plane curves and related invariants
title Fundamental group of plane curves and related invariants
spellingShingle Fundamental group of plane curves and related invariants
Artal Bartolo, Enrique
512.772
plane curves
fundamental group
Geometria algebraica
1201.01 Geometría Algebraica
title_short Fundamental group of plane curves and related invariants
title_full Fundamental group of plane curves and related invariants
title_fullStr Fundamental group of plane curves and related invariants
title_full_unstemmed Fundamental group of plane curves and related invariants
title_sort Fundamental group of plane curves and related invariants
dc.creator.none.fl_str_mv Artal Bartolo, Enrique
Carmona Ruber, Jorge
Cogolludo Agustín, José Ignacio
Luengo Velasco, Ignacio
Melle Hernández, Alejandro
author Artal Bartolo, Enrique
author_facet Artal Bartolo, Enrique
Carmona Ruber, Jorge
Cogolludo Agustín, José Ignacio
Luengo Velasco, Ignacio
Melle Hernández, Alejandro
author_role author
author2 Carmona Ruber, Jorge
Cogolludo Agustín, José Ignacio
Luengo Velasco, Ignacio
Melle Hernández, Alejandro
author2_role author
author
author
author
dc.contributor.none.fl_str_mv Lafuente López, Javier
Pozo Coronado, Luis Miguel
Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 512.772
plane curves
fundamental group
Geometria algebraica
1201.01 Geometría Algebraica
topic 512.772
plane curves
fundamental group
Geometria algebraica
1201.01 Geometría Algebraica
description The article under review contains a study of the topology of a pair (P2,C), where C is an algebraic curve in the complex projective plane. The basic problem is to find invariants which are sensitive enough to distinguish many pairs, and for which there is an algorithm for checking this. The homology of the complement is certainly computable in this sense, but it is too coarse to be really useful. The fundamental group of the complement, by contrast, is very sensitive. The article reviews the Zariski-van Kampen method for finding a presentation for it. However, it is not clear whether the isomorphism problem for this class of groups is solvable. The article surveys many other invariants, such as the Alexander polynomial and characteristic varieties, which are more computable. This last set of invariants was introduced, in this context, by A. S. Libgober [in Applications of algebraic geometry to coding theory, physics and computation (Eilat, 2001), 215–254, Kluwer Acad. Publ., Dordrecht, 2001
publishDate 2000
dc.date.none.fl_str_mv 2000
2000-01-01
2000
2000-01-01
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/20.500.14352/60666
url https://hdl.handle.net/20.500.14352/60666
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 Editorial Complutense
publisher.none.fl_str_mv Editorial Complutense
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
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score 15,300724

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