Horrocks-Mumford holomorphic distributions

Detalhes bibliográficos
Autor(a) principal: Julio Leo Fonseca Quispe
Data de Publicação: 2020
Tipo de documento: Tese
Idioma: eng
Título da fonte: Repositório Institucional da UFMG
Texto Completo: http://hdl.handle.net/1843/38398
https://orcid.org/0000-0003-4490-1778
Resumo: This thesis is devoted to the study of Codimension two Holomorphic Distributions on P4 whose tangent and conormal sheaves are Horrocks-Mumford, that is a stable vector bundle of rank 2, in particular non-decomposable. Our first goal is to describe the geometry of the singular scheme of these distributions. We prove that the singular scheme is a smooth, reduced, irreducible (hence connected) arithmetically Buchsbaum curve. We show that such distributions are non-integrable. Finally, we describe the Moduli space of these distributions, proving that such space is an irreducible quasi-projective variety and we calculate its dimension.
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spelling Maurício Barros Corrêa Júniorhttp://lattes.cnpq.br/8358377857015830José Omegar Calvo-Andradehttp://lattes.cnpq.br/1261389083754328Arnulfo Miguel Rodriguez PeñaIsrael VainsencherMárcio Gomes SoaresMarcos Benevenuto Jardimhttp://lattes.cnpq.br/2564678427634046Julio Leo Fonseca Quispe2021-10-18T01:54:52Z2021-10-18T01:54:52Z2020-03-05http://hdl.handle.net/1843/38398https://orcid.org/0000-0003-4490-1778This thesis is devoted to the study of Codimension two Holomorphic Distributions on P4 whose tangent and conormal sheaves are Horrocks-Mumford, that is a stable vector bundle of rank 2, in particular non-decomposable. Our first goal is to describe the geometry of the singular scheme of these distributions. We prove that the singular scheme is a smooth, reduced, irreducible (hence connected) arithmetically Buchsbaum curve. We show that such distributions are non-integrable. Finally, we describe the Moduli space of these distributions, proving that such space is an irreducible quasi-projective variety and we calculate its dimension.Nesta tese de doutorado nos dedicamos ao estudo de Distribuições Holomorfas de codimensão dois em P4 cujo feixe tangente e conormal é Horrocks-Mumford, isto é, um fibrado vetorial estável, em particular não decomponível de posto 2. Nosso primeiro objetivo é descrever a geometria do esquema singular dessas distribuições. Provamos que o esquema singular é uma curva suave aritmeticamente Buchsbaum, conexa e irredutível. Mostramos que tais distribuições não são integráveis. Finalmente, descrevemos o espaço de Moduli dessas distribuições, provando que tal espaço é uma variedade quasi-projectiva irredutível e calculamos sua dimensão.CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível SuperiorengUniversidade Federal de Minas GeraisPrograma de Pós-Graduação em MatemáticaUFMGBrasilICX - DEPARTAMENTO DE MATEMÁTICAMatemática – TesesFibrados vetoriais – TesesTeoría Global de Folheações e Distribuições Holomorfas – TesesEspaços de Moduli – Teses.Classes de Chern (Geometria Algébrica) - TesesHolomorphic DistributionsHorrocks Mumford vector bundleHorrocks-Mumford holomorphic distributionsDistribuições holomorfas Horrocks-Mumfordinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFMGinstname:Universidade Federal de Minas Gerais (UFMG)instacron:UFMGORIGINALTese_Horrocks Mumford Holomorphic Distributions.pdfTese_Horrocks Mumford Holomorphic Distributions.pdfTese de doutorado. Autor: Julio Leo Fonseca Quispeapplication/pdf969959https://repositorio.ufmg.br/bitstream/1843/38398/1/Tese_Horrocks%20Mumford%20Holomorphic%20Distributions.pdf26537f434a7456ff03f65d56a8fed3eaMD51LICENSElicense.txtlicense.txttext/plain; charset=utf-82118https://repositorio.ufmg.br/bitstream/1843/38398/2/license.txtcda590c95a0b51b4d15f60c9642ca272MD521843/383982021-10-17 22:54:52.449oai:repositorio.ufmg.br:1843/38398TElDRU7Dh0EgREUgRElTVFJJQlVJw4fDg08gTsODTy1FWENMVVNJVkEgRE8gUkVQT1NJVMOTUklPIElOU1RJVFVDSU9OQUwgREEgVUZNRwoKQ29tIGEgYXByZXNlbnRhw6fDo28gZGVzdGEgbGljZW7Dp2EsIHZvY8OqIChvIGF1dG9yIChlcykgb3UgbyB0aXR1bGFyIGRvcyBkaXJlaXRvcyBkZSBhdXRvcikgY29uY2VkZSBhbyBSZXBvc2l0w7NyaW8gSW5zdGl0dWNpb25hbCBkYSBVRk1HIChSSS1VRk1HKSBvIGRpcmVpdG8gbsOjbyBleGNsdXNpdm8gZSBpcnJldm9nw6F2ZWwgZGUgcmVwcm9kdXppciBlL291IGRpc3RyaWJ1aXIgYSBzdWEgcHVibGljYcOnw6NvIChpbmNsdWluZG8gbyByZXN1bW8pIHBvciB0b2RvIG8gbXVuZG8gbm8gZm9ybWF0byBpbXByZXNzbyBlIGVsZXRyw7RuaWNvIGUgZW0gcXVhbHF1ZXIgbWVpbywgaW5jbHVpbmRvIG9zIGZvcm1hdG9zIMOhdWRpbyBvdSB2w61kZW8uCgpWb2PDqiBkZWNsYXJhIHF1ZSBjb25oZWNlIGEgcG9sw610aWNhIGRlIGNvcHlyaWdodCBkYSBlZGl0b3JhIGRvIHNldSBkb2N1bWVudG8gZSBxdWUgY29uaGVjZSBlIGFjZWl0YSBhcyBEaXJldHJpemVzIGRvIFJJLVVGTUcuCgpWb2PDqiBjb25jb3JkYSBxdWUgbyBSZXBvc2l0w7NyaW8gSW5zdGl0dWNpb25hbCBkYSBVRk1HIHBvZGUsIHNlbSBhbHRlcmFyIG8gY29udGXDumRvLCB0cmFuc3BvciBhIHN1YSBwdWJsaWNhw6fDo28gcGFyYSBxdWFscXVlciBtZWlvIG91IGZvcm1hdG8gcGFyYSBmaW5zIGRlIHByZXNlcnZhw6fDo28uCgpWb2PDqiB0YW1iw6ltIGNvbmNvcmRhIHF1ZSBvIFJlcG9zaXTDs3JpbyBJbnN0aXR1Y2lvbmFsIGRhIFVGTUcgcG9kZSBtYW50ZXIgbWFpcyBkZSB1bWEgY8OzcGlhIGRlIHN1YSBwdWJsaWNhw6fDo28gcGFyYSBmaW5zIGRlIHNlZ3VyYW7Dp2EsIGJhY2stdXAgZSBwcmVzZXJ2YcOnw6NvLgoKVm9jw6ogZGVjbGFyYSBxdWUgYSBzdWEgcHVibGljYcOnw6NvIMOpIG9yaWdpbmFsIGUgcXVlIHZvY8OqIHRlbSBvIHBvZGVyIGRlIGNvbmNlZGVyIG9zIGRpcmVpdG9zIGNvbnRpZG9zIG5lc3RhIGxpY2Vuw6dhLiBWb2PDqiB0YW1iw6ltIGRlY2xhcmEgcXVlIG8gZGVww7NzaXRvIGRlIHN1YSBwdWJsaWNhw6fDo28gbsOjbywgcXVlIHNlamEgZGUgc2V1IGNvbmhlY2ltZW50bywgaW5mcmluZ2UgZGlyZWl0b3MgYXV0b3JhaXMgZGUgbmluZ3XDqW0uCgpDYXNvIGEgc3VhIHB1YmxpY2HDp8OjbyBjb250ZW5oYSBtYXRlcmlhbCBxdWUgdm9jw6ogbsOjbyBwb3NzdWkgYSB0aXR1bGFyaWRhZGUgZG9zIGRpcmVpdG9zIGF1dG9yYWlzLCB2b2PDqiBkZWNsYXJhIHF1ZSBvYnRldmUgYSBwZXJtaXNzw6NvIGlycmVzdHJpdGEgZG8gZGV0ZW50b3IgZG9zIGRpcmVpdG9zIGF1dG9yYWlzIHBhcmEgY29uY2VkZXIgYW8gUmVwb3NpdMOzcmlvIEluc3RpdHVjaW9uYWwgZGEgVUZNRyBvcyBkaXJlaXRvcyBhcHJlc2VudGFkb3MgbmVzdGEgbGljZW7Dp2EsIGUgcXVlIGVzc2UgbWF0ZXJpYWwgZGUgcHJvcHJpZWRhZGUgZGUgdGVyY2Vpcm9zIGVzdMOhIGNsYXJhbWVudGUgaWRlbnRpZmljYWRvIGUgcmVjb25oZWNpZG8gbm8gdGV4dG8gb3Ugbm8gY29udGXDumRvIGRhIHB1YmxpY2HDp8OjbyBvcmEgZGVwb3NpdGFkYS4KCkNBU08gQSBQVUJMSUNBw4fDg08gT1JBIERFUE9TSVRBREEgVEVOSEEgU0lETyBSRVNVTFRBRE8gREUgVU0gUEFUUk9Dw41OSU8gT1UgQVBPSU8gREUgVU1BIEFHw4pOQ0lBIERFIEZPTUVOVE8gT1UgT1VUUk8gT1JHQU5JU01PLCBWT0PDiiBERUNMQVJBIFFVRSBSRVNQRUlUT1UgVE9ET1MgRSBRVUFJU1FVRVIgRElSRUlUT1MgREUgUkVWSVPDg08gQ09NTyBUQU1Cw4lNIEFTIERFTUFJUyBPQlJJR0HDh8OVRVMgRVhJR0lEQVMgUE9SIENPTlRSQVRPIE9VIEFDT1JETy4KCk8gUmVwb3NpdMOzcmlvIEluc3RpdHVjaW9uYWwgZGEgVUZNRyBzZSBjb21wcm9tZXRlIGEgaWRlbnRpZmljYXIgY2xhcmFtZW50ZSBvIHNldSBub21lKHMpIG91IG8ocykgbm9tZXMocykgZG8ocykgZGV0ZW50b3IoZXMpIGRvcyBkaXJlaXRvcyBhdXRvcmFpcyBkYSBwdWJsaWNhw6fDo28sIGUgbsOjbyBmYXLDoSBxdWFscXVlciBhbHRlcmHDp8OjbywgYWzDqW0gZGFxdWVsYXMgY29uY2VkaWRhcyBwb3IgZXN0YSBsaWNlbsOnYS4KRepositório de PublicaçõesPUBhttps://repositorio.ufmg.br/oaiopendoar:2021-10-18T01:54:52Repositório Institucional da UFMG - Universidade Federal de Minas Gerais (UFMG)false
dc.title.pt_BR.fl_str_mv Horrocks-Mumford holomorphic distributions
dc.title.alternative.pt_BR.fl_str_mv Distribuições holomorfas Horrocks-Mumford
title Horrocks-Mumford holomorphic distributions
spellingShingle Horrocks-Mumford holomorphic distributions
Julio Leo Fonseca Quispe
Holomorphic Distributions
Horrocks Mumford vector bundle
Matemática – Teses
Fibrados vetoriais – Teses
Teoría Global de Folheações e Distribuições Holomorfas – Teses
Espaços de Moduli – Teses.
Classes de Chern (Geometria Algébrica) - Teses
title_short Horrocks-Mumford holomorphic distributions
title_full Horrocks-Mumford holomorphic distributions
title_fullStr Horrocks-Mumford holomorphic distributions
title_full_unstemmed Horrocks-Mumford holomorphic distributions
title_sort Horrocks-Mumford holomorphic distributions
author Julio Leo Fonseca Quispe
author_facet Julio Leo Fonseca Quispe
author_role author
dc.contributor.advisor1.fl_str_mv Maurício Barros Corrêa Júnior
dc.contributor.advisor1Lattes.fl_str_mv http://lattes.cnpq.br/8358377857015830
dc.contributor.advisor2.fl_str_mv José Omegar Calvo-Andrade
dc.contributor.advisor2Lattes.fl_str_mv http://lattes.cnpq.br/1261389083754328
dc.contributor.referee1.fl_str_mv Arnulfo Miguel Rodriguez Peña
dc.contributor.referee2.fl_str_mv Israel Vainsencher
dc.contributor.referee3.fl_str_mv Márcio Gomes Soares
dc.contributor.referee4.fl_str_mv Marcos Benevenuto Jardim
dc.contributor.authorLattes.fl_str_mv http://lattes.cnpq.br/2564678427634046
dc.contributor.author.fl_str_mv Julio Leo Fonseca Quispe
contributor_str_mv Maurício Barros Corrêa Júnior
José Omegar Calvo-Andrade
Arnulfo Miguel Rodriguez Peña
Israel Vainsencher
Márcio Gomes Soares
Marcos Benevenuto Jardim
dc.subject.por.fl_str_mv Holomorphic Distributions
Horrocks Mumford vector bundle
topic Holomorphic Distributions
Horrocks Mumford vector bundle
Matemática – Teses
Fibrados vetoriais – Teses
Teoría Global de Folheações e Distribuições Holomorfas – Teses
Espaços de Moduli – Teses.
Classes de Chern (Geometria Algébrica) - Teses
dc.subject.other.pt_BR.fl_str_mv Matemática – Teses
Fibrados vetoriais – Teses
Teoría Global de Folheações e Distribuições Holomorfas – Teses
Espaços de Moduli – Teses.
Classes de Chern (Geometria Algébrica) - Teses
description This thesis is devoted to the study of Codimension two Holomorphic Distributions on P4 whose tangent and conormal sheaves are Horrocks-Mumford, that is a stable vector bundle of rank 2, in particular non-decomposable. Our first goal is to describe the geometry of the singular scheme of these distributions. We prove that the singular scheme is a smooth, reduced, irreducible (hence connected) arithmetically Buchsbaum curve. We show that such distributions are non-integrable. Finally, we describe the Moduli space of these distributions, proving that such space is an irreducible quasi-projective variety and we calculate its dimension.
publishDate 2020
dc.date.issued.fl_str_mv 2020-03-05
dc.date.accessioned.fl_str_mv 2021-10-18T01:54:52Z
dc.date.available.fl_str_mv 2021-10-18T01:54:52Z
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.uri.fl_str_mv http://hdl.handle.net/1843/38398
dc.identifier.orcid.pt_BR.fl_str_mv https://orcid.org/0000-0003-4490-1778
url http://hdl.handle.net/1843/38398
https://orcid.org/0000-0003-4490-1778
dc.language.iso.fl_str_mv eng
language eng
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
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
collection Repositório Institucional da UFMG
bitstream.url.fl_str_mv https://repositorio.ufmg.br/bitstream/1843/38398/1/Tese_Horrocks%20Mumford%20Holomorphic%20Distributions.pdf
https://repositorio.ufmg.br/bitstream/1843/38398/2/license.txt
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repository.name.fl_str_mv Repositório Institucional da UFMG - Universidade Federal de Minas Gerais (UFMG)
repository.mail.fl_str_mv
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