Holomorphic vector fields tangent to foliations in dimension three

Detalhes bibliográficos
Autor(a) principal: JUNCA,DANÚBIA
Data de Publicação: 2021
Outros Autores: MOL,ROGÉRIO
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Anais da Academia Brasileira de Ciências (Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652021000600302
Resumo: Abstract We consider a singular holomorphic vector field in a neighborhood of 0 ∈ C 3and suppose that there is a singular holomorphic foliation of codimension one (outside its singular set, given by a holomorphic decomposition of this neighborhood into complex surfaces, called leaves) to which it is tangent. This means that, when both objects are non-singular, the orbits of the vector field are contained in the leaves of the foliation. First we consider the desingularizations of both objects, trying to relate their final models. Then we analyse the situation where the vector field is tangent to three independent foliations.
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spelling Holomorphic vector fields tangent to foliations in dimension threeHolomorphic foliationsholomorphic vector fieldspencil of foliationsinvariant varietiesAbstract We consider a singular holomorphic vector field in a neighborhood of 0 ∈ C 3and suppose that there is a singular holomorphic foliation of codimension one (outside its singular set, given by a holomorphic decomposition of this neighborhood into complex surfaces, called leaves) to which it is tangent. This means that, when both objects are non-singular, the orbits of the vector field are contained in the leaves of the foliation. First we consider the desingularizations of both objects, trying to relate their final models. Then we analyse the situation where the vector field is tangent to three independent foliations.Academia Brasileira de Ciências2021-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652021000600302Anais da Academia Brasileira de Ciências v.93 suppl.3 2021reponame:Anais da Academia Brasileira de Ciências (Online)instname:Academia Brasileira de Ciências (ABC)instacron:ABC10.1590/0001-3765202020181390info:eu-repo/semantics/openAccessJUNCA,DANÚBIAMOL,ROGÉRIOeng2021-09-01T00:00:00Zoai:scielo:S0001-37652021000600302Revistahttp://www.scielo.br/aabchttps://old.scielo.br/oai/scielo-oai.php||aabc@abc.org.br1678-26900001-3765opendoar:2021-09-01T00:00Anais da Academia Brasileira de Ciências (Online) - Academia Brasileira de Ciências (ABC)false
dc.title.none.fl_str_mv Holomorphic vector fields tangent to foliations in dimension three
title Holomorphic vector fields tangent to foliations in dimension three
spellingShingle Holomorphic vector fields tangent to foliations in dimension three
JUNCA,DANÚBIA
Holomorphic foliations
holomorphic vector fields
pencil of foliations
invariant varieties
title_short Holomorphic vector fields tangent to foliations in dimension three
title_full Holomorphic vector fields tangent to foliations in dimension three
title_fullStr Holomorphic vector fields tangent to foliations in dimension three
title_full_unstemmed Holomorphic vector fields tangent to foliations in dimension three
title_sort Holomorphic vector fields tangent to foliations in dimension three
author JUNCA,DANÚBIA
author_facet JUNCA,DANÚBIA
MOL,ROGÉRIO
author_role author
author2 MOL,ROGÉRIO
author2_role author
dc.contributor.author.fl_str_mv JUNCA,DANÚBIA
MOL,ROGÉRIO
dc.subject.por.fl_str_mv Holomorphic foliations
holomorphic vector fields
pencil of foliations
invariant varieties
topic Holomorphic foliations
holomorphic vector fields
pencil of foliations
invariant varieties
description Abstract We consider a singular holomorphic vector field in a neighborhood of 0 ∈ C 3and suppose that there is a singular holomorphic foliation of codimension one (outside its singular set, given by a holomorphic decomposition of this neighborhood into complex surfaces, called leaves) to which it is tangent. This means that, when both objects are non-singular, the orbits of the vector field are contained in the leaves of the foliation. First we consider the desingularizations of both objects, trying to relate their final models. Then we analyse the situation where the vector field is tangent to three independent foliations.
publishDate 2021
dc.date.none.fl_str_mv 2021-01-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652021000600302
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652021000600302
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/0001-3765202020181390
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Academia Brasileira de Ciências
publisher.none.fl_str_mv Academia Brasileira de Ciências
dc.source.none.fl_str_mv Anais da Academia Brasileira de Ciências v.93 suppl.3 2021
reponame:Anais da Academia Brasileira de Ciências (Online)
instname:Academia Brasileira de Ciências (ABC)
instacron:ABC
instname_str Academia Brasileira de Ciências (ABC)
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institution ABC
reponame_str Anais da Academia Brasileira de Ciências (Online)
collection Anais da Academia Brasileira de Ciências (Online)
repository.name.fl_str_mv Anais da Academia Brasileira de Ciências (Online) - Academia Brasileira de Ciências (ABC)
repository.mail.fl_str_mv ||aabc@abc.org.br
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