Holomorphic foliations of degree four on the complex projective space
Autor(a) principal: | |
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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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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 |
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Universidade Federal de Minas Gerais (UFMG) |
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UFMG |
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UFMG |
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Repositório Institucional da UFMG |
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Repositório Institucional da UFMG |
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