Hankel and sub-Hankel determinants ( a detailed study of their polar ideals)
Autor(a) principal: | |
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Data de Publicação: | 2014 |
Tipo de documento: | Tese |
Idioma: | por |
Título da fonte: | Repositório Institucional da UFPE |
Texto Completo: | https://repositorio.ufpe.br/handle/123456789/12195 |
Resumo: | Os resultados desta tese se enquadram na teoria dos polin^omios homaloidais, com ^enfase no caso de determinantes. O objetivo principal e o estudo das propriedades homol ogicas do determinante da matriz gen erica de Hankel e de uma de suas degenera c~oes, como um m etodo de abordar o seu comportamento de natureza homal oide. No caso da matriz de Hankel gen erica, em caracter stica zero, concluimos que o Hessiano do determinante e n~ao nulo (equivalentemente, o mapa polar associado e dominante), mas o determinante n~ao e homal oide. No caso degenerado, sabese que o determinante e homal oide (provado por Cilibert-Russo-Simis [3]); aqui, determinamos os invariantes num ericos e homol ogicos do respectivo ideal gradiente (polar), esses podendo ser usados para simpli car algumas passagens no argumento de [3]. Os principais resultados da tese s~ao baseados em ferramentas n~ao triviais da algebra comutativa e a natureza do uso dessas ferramentas e um dos recursos importantes desta tese. |
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Maral, MostafazadehfardSimis, Aron 2015-03-12T16:03:51Z2015-03-12T16:03:51Z2014-01-31https://repositorio.ufpe.br/handle/123456789/12195Os resultados desta tese se enquadram na teoria dos polin^omios homaloidais, com ^enfase no caso de determinantes. O objetivo principal e o estudo das propriedades homol ogicas do determinante da matriz gen erica de Hankel e de uma de suas degenera c~oes, como um m etodo de abordar o seu comportamento de natureza homal oide. No caso da matriz de Hankel gen erica, em caracter stica zero, concluimos que o Hessiano do determinante e n~ao nulo (equivalentemente, o mapa polar associado e dominante), mas o determinante n~ao e homal oide. No caso degenerado, sabese que o determinante e homal oide (provado por Cilibert-Russo-Simis [3]); aqui, determinamos os invariantes num ericos e homol ogicos do respectivo ideal gradiente (polar), esses podendo ser usados para simpli car algumas passagens no argumento de [3]. Os principais resultados da tese s~ao baseados em ferramentas n~ao triviais da algebra comutativa e a natureza do uso dessas ferramentas e um dos recursos importantes desta tese.CNPqporUniversidade Federal de PernambucoAttribution-NonCommercial-NoDerivs 3.0 Brazilhttp://creativecommons.org/licenses/by-nc-nd/3.0/br/info:eu-repo/semantics/openAccessMatriz de HankelPolinômio homaloideMapa polarIdeal gradienteHessianoSizigias linearesÁlgebra simetricaÁlgebra de ReesEqua ções de Pl uckerHankel and sub-Hankel determinants ( a detailed study of their polar ideals)info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisreponame:Repositório Institucional da UFPEinstname:Universidade Federal de Pernambuco (UFPE)instacron:UFPETHUMBNAILTESE Maral Mostafazadehfard.pdf.jpgTESE Maral Mostafazadehfard.pdf.jpgGenerated Thumbnailimage/jpeg1343https://repositorio.ufpe.br/bitstream/123456789/12195/5/TESE%20Maral%20Mostafazadehfard.pdf.jpg8dec9416d1ab3cf09aedb400b22e78b1MD55ORIGINALTESE Maral Mostafazadehfard.pdfTESE Maral Mostafazadehfard.pdfapplication/pdf759835https://repositorio.ufpe.br/bitstream/123456789/12195/1/TESE%20Maral%20Mostafazadehfard.pdf0db918f26f85cab03090a30fba1d2b36MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; 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dc.title.pt_BR.fl_str_mv |
Hankel and sub-Hankel determinants ( a detailed study of their polar ideals) |
title |
Hankel and sub-Hankel determinants ( a detailed study of their polar ideals) |
spellingShingle |
Hankel and sub-Hankel determinants ( a detailed study of their polar ideals) Maral, Mostafazadehfard Matriz de Hankel Polinômio homaloide Mapa polar Ideal gradiente Hessiano Sizigias lineares Álgebra simetrica Álgebra de Rees Equa ções de Pl ucker |
title_short |
Hankel and sub-Hankel determinants ( a detailed study of their polar ideals) |
title_full |
Hankel and sub-Hankel determinants ( a detailed study of their polar ideals) |
title_fullStr |
Hankel and sub-Hankel determinants ( a detailed study of their polar ideals) |
title_full_unstemmed |
Hankel and sub-Hankel determinants ( a detailed study of their polar ideals) |
title_sort |
Hankel and sub-Hankel determinants ( a detailed study of their polar ideals) |
author |
Maral, Mostafazadehfard |
author_facet |
Maral, Mostafazadehfard |
author_role |
author |
dc.contributor.author.fl_str_mv |
Maral, Mostafazadehfard |
dc.contributor.advisor1.fl_str_mv |
Simis, Aron |
contributor_str_mv |
Simis, Aron |
dc.subject.por.fl_str_mv |
Matriz de Hankel Polinômio homaloide Mapa polar Ideal gradiente Hessiano Sizigias lineares Álgebra simetrica Álgebra de Rees Equa ções de Pl ucker |
topic |
Matriz de Hankel Polinômio homaloide Mapa polar Ideal gradiente Hessiano Sizigias lineares Álgebra simetrica Álgebra de Rees Equa ções de Pl ucker |
description |
Os resultados desta tese se enquadram na teoria dos polin^omios homaloidais, com ^enfase no caso de determinantes. O objetivo principal e o estudo das propriedades homol ogicas do determinante da matriz gen erica de Hankel e de uma de suas degenera c~oes, como um m etodo de abordar o seu comportamento de natureza homal oide. No caso da matriz de Hankel gen erica, em caracter stica zero, concluimos que o Hessiano do determinante e n~ao nulo (equivalentemente, o mapa polar associado e dominante), mas o determinante n~ao e homal oide. No caso degenerado, sabese que o determinante e homal oide (provado por Cilibert-Russo-Simis [3]); aqui, determinamos os invariantes num ericos e homol ogicos do respectivo ideal gradiente (polar), esses podendo ser usados para simpli car algumas passagens no argumento de [3]. Os principais resultados da tese s~ao baseados em ferramentas n~ao triviais da algebra comutativa e a natureza do uso dessas ferramentas e um dos recursos importantes desta tese. |
publishDate |
2014 |
dc.date.issued.fl_str_mv |
2014-01-31 |
dc.date.accessioned.fl_str_mv |
2015-03-12T16:03:51Z |
dc.date.available.fl_str_mv |
2015-03-12T16:03:51Z |
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 |
https://repositorio.ufpe.br/handle/123456789/12195 |
url |
https://repositorio.ufpe.br/handle/123456789/12195 |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.rights.driver.fl_str_mv |
Attribution-NonCommercial-NoDerivs 3.0 Brazil http://creativecommons.org/licenses/by-nc-nd/3.0/br/ info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Attribution-NonCommercial-NoDerivs 3.0 Brazil http://creativecommons.org/licenses/by-nc-nd/3.0/br/ |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Universidade Federal de Pernambuco |
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) instacron:UFPE |
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UFPE |
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UFPE |
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Repositório Institucional da UFPE |
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Repositório Institucional da UFPE |
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