Holomorphic foliations of degree four on the complex projective space

Detalhes bibliográficos
Autor(a) principal: Vângellis Oliveira Sagnori Maia
Data de Publicação: 2022
Tipo de documento: Dissertação
Idioma: eng
Título da fonte: Repositório Institucional da UFMG
Texto Completo: http://hdl.handle.net/1843/68083
https://orcid.org/0009-0003-6226-8272
Resumo: In this work, we study holomorphic foliations of degree four on complex projective space $\p^n$, where $n\geq 3$, with a special focus on obtaining a structural theorem for these foliations. Furthermore, for a foliation $\f$ of degree $d\geq 4$ with a sufficiently high $k^{th}$-jet, we prove that either $\f$ is transversely affine outside a compact hypersurface, or $\f$ is transversely projective outside a compact hypersurface, or $\f$ is the pull-back of a foliation on $\p^2$ by a rational map.
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spelling Arturo Ulises Fernández Pérezhttp://lattes.cnpq.br/2237596477064578Arnulfo Miguel Rodriguez PeñaGilcione Nonato CostaJosé Omegar Calvo AndradeMaurício Barros Corrêa Júniorhttp://lattes.cnpq.br/4194104165120422Vângellis Oliveira Sagnori Maia2024-05-03T21:39:11Z2024-05-03T21:39:11Z2022-03-25http://hdl.handle.net/1843/68083https://orcid.org/0009-0003-6226-8272In this work, we study holomorphic foliations of degree four on complex projective space $\p^n$, where $n\geq 3$, with a special focus on obtaining a structural theorem for these foliations. Furthermore, for a foliation $\f$ of degree $d\geq 4$ with a sufficiently high $k^{th}$-jet, we prove that either $\f$ is transversely affine outside a compact hypersurface, or $\f$ is transversely projective outside a compact hypersurface, or $\f$ is the pull-back of a foliation on $\p^2$ by a rational map.Neste trabalho, estudaremos folheações holomorfas de grau quatro no espaço projetivo complexo $\mathbb{P}^n$, com $n \geq 3$, com especial foco em obter um teorema estrutural para essas folheações. Mais ainda, para uma folheação $\mathcal{F}$ de grau $d \geq 4$ com $k^{\circ}$-jato suficientente alto, provamos que $\mathcal{F}$ é transversalmente afim fora de uma hipersuperfície compacta, ou $\mathcal{F}$ é transversalmente projetiva fora de uma hipersuperfície compacta, ou $\mathcal{F}$ é o Pull-back de uma folheação em $\mathbb{P}^2$ por um mapa racional.CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível SuperiorengUniversidade Federal de Minas GeraisPrograma de Pós-Graduação em MatemáticaUFMGBrasilICX - DEPARTAMENTO DE MATEMÁTICAhttp://creativecommons.org/licenses/by/3.0/pt/info:eu-repo/semantics/openAccessMatemática – TesesFolheações (Matemática) – TesesSeqüências (Matemática) – TesesHolomorphic FoliationRational First IntegralAffine Transverse StructurePure Projective Transverse StructurePull-back Of FoliationsGodbillon-Vey SequencesHolomorphic foliations of degree four on the complex projective spaceinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisreponame:Repositório Institucional da UFMGinstname:Universidade Federal de Minas Gerais (UFMG)instacron:UFMGORIGINALHolomorphic foliations of degree four on the complex projective space.pdfHolomorphic foliations of degree four on the complex projective space.pdfapplication/pdf829725https://repositorio.ufmg.br/bitstream/1843/68083/6/Holomorphic%20foliations%20of%20degree%20four%20on%20the%20complex%20projective%20space.pdfda364e818ec6be983733d44549cc8dfdMD56CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8914https://repositorio.ufmg.br/bitstream/1843/68083/7/license_rdff9944a358a0c32770bd9bed185bb5395MD57LICENSElicense.txtlicense.txttext/plain; charset=utf-82118https://repositorio.ufmg.br/bitstream/1843/68083/8/license.txtcda590c95a0b51b4d15f60c9642ca272MD581843/680832024-05-03 18:39:13.407oai:repositorio.ufmg.br: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ório de PublicaçõesPUBhttps://repositorio.ufmg.br/oaiopendoar:2024-05-03T21:39:13Repositório Institucional da UFMG - Universidade Federal de Minas Gerais (UFMG)false
dc.title.pt_BR.fl_str_mv Holomorphic foliations of degree four on the complex projective space
title Holomorphic foliations of degree four on the complex projective space
spellingShingle Holomorphic foliations of degree four on the complex projective space
Vângellis Oliveira Sagnori Maia
Holomorphic Foliation
Rational First Integral
Affine Transverse Structure
Pure Projective Transverse Structure
Pull-back Of Foliations
Godbillon-Vey Sequences
Matemática – Teses
Folheações (Matemática) – Teses
Seqüências (Matemática) – Teses
title_short Holomorphic foliations of degree four on the complex projective space
title_full Holomorphic foliations of degree four on the complex projective space
title_fullStr Holomorphic foliations of degree four on the complex projective space
title_full_unstemmed Holomorphic foliations of degree four on the complex projective space
title_sort Holomorphic foliations of degree four on the complex projective space
author Vângellis Oliveira Sagnori Maia
author_facet Vângellis Oliveira Sagnori Maia
author_role author
dc.contributor.advisor1.fl_str_mv Arturo Ulises Fernández Pérez
dc.contributor.advisor1Lattes.fl_str_mv http://lattes.cnpq.br/2237596477064578
dc.contributor.referee1.fl_str_mv Arnulfo Miguel Rodriguez Peña
dc.contributor.referee2.fl_str_mv Gilcione Nonato Costa
dc.contributor.referee3.fl_str_mv José Omegar Calvo Andrade
dc.contributor.referee4.fl_str_mv Maurício Barros Corrêa Júnior
dc.contributor.authorLattes.fl_str_mv http://lattes.cnpq.br/4194104165120422
dc.contributor.author.fl_str_mv Vângellis Oliveira Sagnori Maia
contributor_str_mv Arturo Ulises Fernández Pérez
Arnulfo Miguel Rodriguez Peña
Gilcione Nonato Costa
José Omegar Calvo Andrade
Maurício Barros Corrêa Júnior
dc.subject.por.fl_str_mv Holomorphic Foliation
Rational First Integral
Affine Transverse Structure
Pure Projective Transverse Structure
Pull-back Of Foliations
Godbillon-Vey Sequences
topic Holomorphic Foliation
Rational First Integral
Affine Transverse Structure
Pure Projective Transverse Structure
Pull-back Of Foliations
Godbillon-Vey Sequences
Matemática – Teses
Folheações (Matemática) – Teses
Seqüências (Matemática) – Teses
dc.subject.other.pt_BR.fl_str_mv Matemática – Teses
Folheações (Matemática) – Teses
Seqüências (Matemática) – Teses
description In this work, we study holomorphic foliations of degree four on complex projective space $\p^n$, where $n\geq 3$, with a special focus on obtaining a structural theorem for these foliations. Furthermore, for a foliation $\f$ of degree $d\geq 4$ with a sufficiently high $k^{th}$-jet, we prove that either $\f$ is transversely affine outside a compact hypersurface, or $\f$ is transversely projective outside a compact hypersurface, or $\f$ is the pull-back of a foliation on $\p^2$ by a rational map.
publishDate 2022
dc.date.issued.fl_str_mv 2022-03-25
dc.date.accessioned.fl_str_mv 2024-05-03T21:39:11Z
dc.date.available.fl_str_mv 2024-05-03T21:39:11Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/masterThesis
format masterThesis
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/1843/68083
dc.identifier.orcid.pt_BR.fl_str_mv https://orcid.org/0009-0003-6226-8272
url http://hdl.handle.net/1843/68083
https://orcid.org/0009-0003-6226-8272
dc.language.iso.fl_str_mv eng
language eng
dc.rights.driver.fl_str_mv http://creativecommons.org/licenses/by/3.0/pt/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/3.0/pt/
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Universidade Federal de Minas Gerais
dc.publisher.program.fl_str_mv Programa de Pós-Graduação em Matemática
dc.publisher.initials.fl_str_mv UFMG
dc.publisher.country.fl_str_mv Brasil
dc.publisher.department.fl_str_mv ICX - DEPARTAMENTO DE MATEMÁTICA
publisher.none.fl_str_mv Universidade Federal de Minas Gerais
dc.source.none.fl_str_mv reponame:Repositório Institucional da UFMG
instname:Universidade Federal de Minas Gerais (UFMG)
instacron:UFMG
instname_str Universidade Federal de Minas Gerais (UFMG)
instacron_str UFMG
institution UFMG
reponame_str Repositório Institucional da UFMG
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bitstream.url.fl_str_mv https://repositorio.ufmg.br/bitstream/1843/68083/6/Holomorphic%20foliations%20of%20degree%20four%20on%20the%20complex%20projective%20space.pdf
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