Topics on perfect ideals of codimension two

Detalhes bibliográficos
Ano de defesa: 2025
Autor(a) principal: OLIVEIRA, Geisa Gama
Orientador(a): SIMIS, Aron
Banca de defesa: Não Informado pela instituição
Tipo de documento: Tese
Tipo de acesso: Acesso aberto
Idioma: eng
Instituição de defesa: Universidade Federal de Pernambuco
Programa de Pós-Graduação: Programa de Pos Graduacao em Matematica
Departamento: Não Informado pela instituição
País: Brasil
Palavras-chave em Português:
Monomial ideals
Plane reduced points
Special fiber
Perfect ideal of codimension two
Rees algebra
Cohen-Macaulay
Link de acesso: https://repositorio.ufpe.br/handle/123456789/68301
Resumo: In this work, we are interested in perfect ideals I of codimension two in a polynomial ring R over a field of characteristic zero. The overall interest is on the homological nature of the main algebras related to the Hilbert-Burch syzygy matrix associated to I, in particular on the Cohen-Macaulay property of the Rees algebra and the special fiber of I. We develop this study in three contexts: monomial ideals, ideals defined by the 2-minors of homogeneous 3 × 2 matrices, and the defining ideal of a finite set of reduced points in projective 2-space. In addition, we investigate geometric aspects related to these ideals, focusing on how their algebraic properties are reflected in the associated rational maps.
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spelling OLIVEIRA, Geisa Gamahttp://lattes.cnpq.br/5111791472406550http://lattes.cnpq.br/8415377033264469http://lattes.cnpq.br/9937925412759644https://orcid.org/0009-0009-3596-6570https://orcid.org/0000-0002-2848-8509https://orcid.org/0000-0001-5823-8394SIMIS, AronRAMOS, Zaqueu2026-02-10T17:15:16Z2026-02-10T17:15:16Z2025-11-27OLIVEIRA, Geisa Gama. Topics on perfect ideals of codimension two. 2025. Tese (Doutorado em Matemática) - Universidade Federal de Pernambuco, Recife, 2025.https://repositorio.ufpe.br/handle/123456789/68301In this work, we are interested in perfect ideals I of codimension two in a polynomial ring R over a field of characteristic zero. The overall interest is on the homological nature of the main algebras related to the Hilbert-Burch syzygy matrix associated to I, in particular on the Cohen-Macaulay property of the Rees algebra and the special fiber of I. We develop this study in three contexts: monomial ideals, ideals defined by the 2-minors of homogeneous 3 × 2 matrices, and the defining ideal of a finite set of reduced points in projective 2-space. In addition, we investigate geometric aspects related to these ideals, focusing on how their algebraic properties are reflected in the associated rational maps.CAPES.engUniversidade Federal de PernambucoPrograma de Pos Graduacao em MatematicaUFPEBrasilhttps://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessMonomial idealsPlane reduced pointsSpecial fiberPerfect ideal of codimension twoRees algebraCohen-MacaulayTopics on perfect ideals of codimension twoinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisdoutoradoreponame:Repositório Institucional da UFPEinstname:Universidade Federal de Pernambuco (UFPE)instacron:UFPELICENSElicense.txtlicense.txttext/plain; charset=utf-82362https://repositorio.ufpe.br/bitstream/123456789/68301/2/license.txt5e89a1613ddc8510c6576f4b23a78973MD52ORIGINALTESE Geisa Gama Oliveira.pdfTESE Geisa Gama Oliveira.pdfapplication/pdf897353https://repositorio.ufpe.br/bitstream/123456789/68301/1/TESE%20Geisa%20Gama%20Oliveira.pdf403d673d4da846f03911d919c26e56d5MD51123456789/683012026-02-10 14:15:19.838oai:repositorio.ufpe.br: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Repositório InstitucionalPUBhttps://repositorio.ufpe.br/oai/requestattena@ufpe.bropendoar:22212026-02-10T17:15:19Repositório Institucional da UFPE - Universidade Federal de Pernambuco (UFPE)false
dc.title.pt_BR.fl_str_mv Topics on perfect ideals of codimension two
title Topics on perfect ideals of codimension two
spellingShingle Topics on perfect ideals of codimension two
OLIVEIRA, Geisa Gama
Monomial ideals
Plane reduced points
Special fiber
Perfect ideal of codimension two
Rees algebra
Cohen-Macaulay
title_short Topics on perfect ideals of codimension two
title_full Topics on perfect ideals of codimension two
title_fullStr Topics on perfect ideals of codimension two
title_full_unstemmed Topics on perfect ideals of codimension two
title_sort Topics on perfect ideals of codimension two
author OLIVEIRA, Geisa Gama
author_facet OLIVEIRA, Geisa Gama
author_role author
dc.contributor.authorLattes.pt_BR.fl_str_mv http://lattes.cnpq.br/5111791472406550
dc.contributor.advisorLattes.pt_BR.fl_str_mv http://lattes.cnpq.br/8415377033264469
dc.contributor.advisor-coLattes.pt_BR.fl_str_mv http://lattes.cnpq.br/9937925412759644
dc.contributor.authorORCID.pt_BR.fl_str_mv https://orcid.org/0009-0009-3596-6570
dc.contributor.advisorORCID.pt_BR.fl_str_mv https://orcid.org/0000-0002-2848-8509
dc.contributor.advisor-coORCID.pt_BR.fl_str_mv https://orcid.org/0000-0001-5823-8394
dc.contributor.author.fl_str_mv OLIVEIRA, Geisa Gama
dc.contributor.advisor1.fl_str_mv SIMIS, Aron
dc.contributor.advisor-co1.fl_str_mv RAMOS, Zaqueu
contributor_str_mv SIMIS, Aron
RAMOS, Zaqueu
dc.subject.por.fl_str_mv Monomial ideals
Plane reduced points
Special fiber
Perfect ideal of codimension two
Rees algebra
Cohen-Macaulay
topic Monomial ideals
Plane reduced points
Special fiber
Perfect ideal of codimension two
Rees algebra
Cohen-Macaulay
description In this work, we are interested in perfect ideals I of codimension two in a polynomial ring R over a field of characteristic zero. The overall interest is on the homological nature of the main algebras related to the Hilbert-Burch syzygy matrix associated to I, in particular on the Cohen-Macaulay property of the Rees algebra and the special fiber of I. We develop this study in three contexts: monomial ideals, ideals defined by the 2-minors of homogeneous 3 × 2 matrices, and the defining ideal of a finite set of reduced points in projective 2-space. In addition, we investigate geometric aspects related to these ideals, focusing on how their algebraic properties are reflected in the associated rational maps.
publishDate 2025
dc.date.issued.fl_str_mv 2025-11-27
dc.date.accessioned.fl_str_mv 2026-02-10T17:15:16Z
dc.date.available.fl_str_mv 2026-02-10T17:15:16Z
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 OLIVEIRA, Geisa Gama. Topics on perfect ideals of codimension two. 2025. Tese (Doutorado em Matemática) - Universidade Federal de Pernambuco, Recife, 2025.
dc.identifier.uri.fl_str_mv https://repositorio.ufpe.br/handle/123456789/68301
identifier_str_mv OLIVEIRA, Geisa Gama. Topics on perfect ideals of codimension two. 2025. Tese (Doutorado em Matemática) - Universidade Federal de Pernambuco, Recife, 2025.
url https://repositorio.ufpe.br/handle/123456789/68301
dc.language.iso.fl_str_mv eng
language eng
dc.rights.driver.fl_str_mv https://creativecommons.org/licenses/by-nc-nd/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Universidade Federal de Pernambuco
dc.publisher.program.fl_str_mv Programa de Pos Graduacao em Matematica
dc.publisher.initials.fl_str_mv UFPE
dc.publisher.country.fl_str_mv Brasil
publisher.none.fl_str_mv Universidade Federal de Pernambuco
dc.source.none.fl_str_mv reponame:Repositório Institucional da UFPE
instname:Universidade Federal de Pernambuco (UFPE)
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instname_str Universidade Federal de Pernambuco (UFPE)
instacron_str UFPE
institution UFPE
reponame_str Repositório Institucional da UFPE
collection Repositório Institucional da UFPE
bitstream.url.fl_str_mv https://repositorio.ufpe.br/bitstream/123456789/68301/2/license.txt
https://repositorio.ufpe.br/bitstream/123456789/68301/1/TESE%20Geisa%20Gama%20Oliveira.pdf
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