Lipschitz geometry of complex plane algebraic curves.

Detalhes bibliográficos
Ano de defesa: 2020
Autor(a) principal: Targino, Renato Oliveira
Orientador(a): Fernandes, Alexandre César Gurgel
Banca de defesa: Não Informado pela instituição
Tipo de documento: Tese
Tipo de acesso: Acesso aberto
Idioma: por
Instituição de defesa: Não Informado pela instituição
Programa de Pós-Graduação: Não Informado pela instituição
Departamento: Não Informado pela instituição
País: Não Informado pela instituição
Palavras-chave em Português:
Curvas algébricas planas e complexas
Geometria Lipschitz
Plane algebraic curves
Lipschitz geometry
Link de acesso: http://www.repositorio.ufc.br/handle/riufc/50537
Resumo: We present the complete classification of complex plane algebraic curves, equipped with the induced Euclidean metric, up to global bilipschitz homeomorphism. In particular, we prove a theorem giving a complete classification of the Lipschitz geometry at infinity of complex algebraic plane curves. We synthesize combinatorial objects that encode both Lipschitz geometry and Lipschitz geometry at infinity of complex algebraic plane curves.
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spelling Targino, Renato OliveiraPichon, AnneFernandes, Alexandre César Gurgel2020-03-05T16:51:07Z2020-03-05T16:51:07Z2020-02-13TARGINO, Renato Oliveira. Lipschitz geometry of complex plane algebraic curves. 2020. 54 f. Tese (Doutorado em Matemática) – Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2020.http://www.repositorio.ufc.br/handle/riufc/50537We present the complete classification of complex plane algebraic curves, equipped with the induced Euclidean metric, up to global bilipschitz homeomorphism. In particular, we prove a theorem giving a complete classification of the Lipschitz geometry at infinity of complex algebraic plane curves. We synthesize combinatorial objects that encode both Lipschitz geometry and Lipschitz geometry at infinity of complex algebraic plane curves.Apresentamos a classificação completa de curvas algébricas planas e complexas, com métrica euclidiana induzida, a menos de homeomorfismo bilipschitz. Em particular, provamos um teorema que fornece a classificação completa da geometria Lipschitz no infinito de curvas planas algébricas complexas. Sintetizamos objetos combinatórios que codificam tanto a geometria Lipschitz como a geometria Lipschitz no infinito de curvas algébricas planas e complexas.Curvas algébricas planas e complexasGeometria LipschitzPlane algebraic curvesLipschitz geometryLipschitz geometry of complex plane algebraic curves.Lipschitz geometry of complex plane algebraic curves.info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisporreponame:Repositório Institucional da Universidade Federal do Ceará (UFC)instname:Universidade Federal do Ceará (UFC)instacron:UFCinfo:eu-repo/semantics/openAccessORIGINAL2020_tese_rotargino.pdf2020_tese_rotargino.pdftese targinoapplication/pdf562026http://repositorio.ufc.br/bitstream/riufc/50537/1/2020_tese_rotargino.pdf300917fbb6378321b3d9270d3168c449MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81748http://repositorio.ufc.br/bitstream/riufc/50537/2/license.txt8a4605be74aa9ea9d79846c1fba20a33MD52riufc/505372020-03-05 13:51:08.001oai:repositorio.ufc.br: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Repositório InstitucionalPUBhttp://www.repositorio.ufc.br/ri-oai/requestbu@ufc.br || repositorio@ufc.bropendoar:2020-03-05T16:51:08Repositório Institucional da Universidade Federal do Ceará (UFC) - Universidade Federal do Ceará (UFC)false
dc.title.pt_BR.fl_str_mv Lipschitz geometry of complex plane algebraic curves.
dc.title.en.pt_BR.fl_str_mv Lipschitz geometry of complex plane algebraic curves.
title Lipschitz geometry of complex plane algebraic curves.
spellingShingle Lipschitz geometry of complex plane algebraic curves.
Targino, Renato Oliveira
Curvas algébricas planas e complexas
Geometria Lipschitz
Plane algebraic curves
Lipschitz geometry
title_short Lipschitz geometry of complex plane algebraic curves.
title_full Lipschitz geometry of complex plane algebraic curves.
title_fullStr Lipschitz geometry of complex plane algebraic curves.
title_full_unstemmed Lipschitz geometry of complex plane algebraic curves.
title_sort Lipschitz geometry of complex plane algebraic curves.
author Targino, Renato Oliveira
author_facet Targino, Renato Oliveira
author_role author
dc.contributor.co-advisor.none.fl_str_mv Pichon, Anne
dc.contributor.author.fl_str_mv Targino, Renato Oliveira
dc.contributor.advisor1.fl_str_mv Fernandes, Alexandre César Gurgel
contributor_str_mv Fernandes, Alexandre César Gurgel
dc.subject.por.fl_str_mv Curvas algébricas planas e complexas
Geometria Lipschitz
Plane algebraic curves
Lipschitz geometry
topic Curvas algébricas planas e complexas
Geometria Lipschitz
Plane algebraic curves
Lipschitz geometry
description We present the complete classification of complex plane algebraic curves, equipped with the induced Euclidean metric, up to global bilipschitz homeomorphism. In particular, we prove a theorem giving a complete classification of the Lipschitz geometry at infinity of complex algebraic plane curves. We synthesize combinatorial objects that encode both Lipschitz geometry and Lipschitz geometry at infinity of complex algebraic plane curves.
publishDate 2020
dc.date.accessioned.fl_str_mv 2020-03-05T16:51:07Z
dc.date.available.fl_str_mv 2020-03-05T16:51:07Z
dc.date.issued.fl_str_mv 2020-02-13
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/doctoralThesis
format doctoralThesis
status_str publishedVersion
dc.identifier.citation.fl_str_mv TARGINO, Renato Oliveira. Lipschitz geometry of complex plane algebraic curves. 2020. 54 f. Tese (Doutorado em Matemática) – Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2020.
dc.identifier.uri.fl_str_mv http://www.repositorio.ufc.br/handle/riufc/50537
identifier_str_mv TARGINO, Renato Oliveira. Lipschitz geometry of complex plane algebraic curves. 2020. 54 f. Tese (Doutorado em Matemática) – Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2020.
url http://www.repositorio.ufc.br/handle/riufc/50537
dc.language.iso.fl_str_mv por
language por
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.source.none.fl_str_mv reponame:Repositório Institucional da Universidade Federal do Ceará (UFC)
instname:Universidade Federal do Ceará (UFC)
instacron:UFC
instname_str Universidade Federal do Ceará (UFC)
instacron_str UFC
institution UFC
reponame_str Repositório Institucional da Universidade Federal do Ceará (UFC)
collection Repositório Institucional da Universidade Federal do Ceará (UFC)
bitstream.url.fl_str_mv http://repositorio.ufc.br/bitstream/riufc/50537/1/2020_tese_rotargino.pdf
http://repositorio.ufc.br/bitstream/riufc/50537/2/license.txt
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repository.name.fl_str_mv Repositório Institucional da Universidade Federal do Ceará (UFC) - Universidade Federal do Ceará (UFC)
repository.mail.fl_str_mv bu@ufc.br || repositorio@ufc.br
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