Resolution of Singularities of Germs of Curves

Detalhes bibliográficos
Autor(a) principal: Canarias, Tiago Alexandre Espiga
Data de Publicação: 2023
Tipo de documento: Dissertação
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10362/161214
Resumo: Our main goal in this work is to introduce the reader to a subarea of algebraic geometry known as local analytic geometry. In this thesis we will give some general concepts, going in depth into the study of irreducible curves and giving algorithms in the computer program SINGULAR for the computation of the examples presented in this thesis. Most of the work will use a well-known mathematical object called Puiseux series, a tool that allows us to parameterize analytic curves locally, hence its importance for the resolution of singularities. This work provides a detailed description of how Puiseux characteristics evolve after a finite number of blow-ups.
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spelling Resolution of Singularities of Germs of CurvesLocal Analytic GeometryPuiseux CharacteristicsResolution of SingularitiesSpace CurvesBlow-upsDomínio/Área Científica::Ciências Naturais::MatemáticasOur main goal in this work is to introduce the reader to a subarea of algebraic geometry known as local analytic geometry. In this thesis we will give some general concepts, going in depth into the study of irreducible curves and giving algorithms in the computer program SINGULAR for the computation of the examples presented in this thesis. Most of the work will use a well-known mathematical object called Puiseux series, a tool that allows us to parameterize analytic curves locally, hence its importance for the resolution of singularities. This work provides a detailed description of how Puiseux characteristics evolve after a finite number of blow-ups.Cabral, JoãoCasimiro, AnaRUNCanarias, Tiago Alexandre Espiga2023-12-13T19:25:36Z2023-052023-05-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisapplication/pdfhttp://hdl.handle.net/10362/161214enginfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-03-11T05:44:04Zoai:run.unl.pt:10362/161214Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:58:26.207641Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Resolution of Singularities of Germs of Curves
title Resolution of Singularities of Germs of Curves
spellingShingle Resolution of Singularities of Germs of Curves
Canarias, Tiago Alexandre Espiga
Local Analytic Geometry
Puiseux Characteristics
Resolution of Singularities
Space Curves
Blow-ups
Domínio/Área Científica::Ciências Naturais::Matemáticas
title_short Resolution of Singularities of Germs of Curves
title_full Resolution of Singularities of Germs of Curves
title_fullStr Resolution of Singularities of Germs of Curves
title_full_unstemmed Resolution of Singularities of Germs of Curves
title_sort Resolution of Singularities of Germs of Curves
author Canarias, Tiago Alexandre Espiga
author_facet Canarias, Tiago Alexandre Espiga
author_role author
dc.contributor.none.fl_str_mv Cabral, João
Casimiro, Ana
RUN
dc.contributor.author.fl_str_mv Canarias, Tiago Alexandre Espiga
dc.subject.por.fl_str_mv Local Analytic Geometry
Puiseux Characteristics
Resolution of Singularities
Space Curves
Blow-ups
Domínio/Área Científica::Ciências Naturais::Matemáticas
topic Local Analytic Geometry
Puiseux Characteristics
Resolution of Singularities
Space Curves
Blow-ups
Domínio/Área Científica::Ciências Naturais::Matemáticas
description Our main goal in this work is to introduce the reader to a subarea of algebraic geometry known as local analytic geometry. In this thesis we will give some general concepts, going in depth into the study of irreducible curves and giving algorithms in the computer program SINGULAR for the computation of the examples presented in this thesis. Most of the work will use a well-known mathematical object called Puiseux series, a tool that allows us to parameterize analytic curves locally, hence its importance for the resolution of singularities. This work provides a detailed description of how Puiseux characteristics evolve after a finite number of blow-ups.
publishDate 2023
dc.date.none.fl_str_mv 2023-12-13T19:25:36Z
2023-05
2023-05-01T00:00:00Z
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/10362/161214
url http://hdl.handle.net/10362/161214
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.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
repository.mail.fl_str_mv
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