Finitely curved orbits of complex polynomial vector fields

Detalhes bibliográficos
Autor(a) principal: Mafra,Albetã C.
Data de Publicação: 2007
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=S0001-37652007000100002
Resumo: This note is about the geometry of holomorphic foliations. Let X be a polynomial vector field with isolated singularities on C². We announce some results regarding two problems: 1. Given a finitely curved orbit L of X, under which conditions is L algebraic? 2. If X has some non-algebraic finitely curved orbit L what is the classification of X? Problem 1 is related to the following question: Let C <FONT FACE=Symbol>Ì</FONT> C² be a holomorphic curve which has finite total Gaussian curvature. IsC contained in an algebraic curve?
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spelling Finitely curved orbits of complex polynomial vector fieldsHolomorphic foliationspolynomial vector fieldsalgebraic curvesfinite total curvatureThis note is about the geometry of holomorphic foliations. Let X be a polynomial vector field with isolated singularities on C². We announce some results regarding two problems: 1. Given a finitely curved orbit L of X, under which conditions is L algebraic? 2. If X has some non-algebraic finitely curved orbit L what is the classification of X? Problem 1 is related to the following question: Let C <FONT FACE=Symbol>Ì</FONT> C² be a holomorphic curve which has finite total Gaussian curvature. IsC contained in an algebraic curve?Academia Brasileira de Ciências2007-03-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652007000100002Anais da Academia Brasileira de Ciências v.79 n.1 2007reponame:Anais da Academia Brasileira de Ciências (Online)instname:Academia Brasileira de Ciências (ABC)instacron:ABC10.1590/S0001-37652007000100002info:eu-repo/semantics/openAccessMafra,Albetã C.eng2007-03-23T00:00:00Zoai:scielo:S0001-37652007000100002Revistahttp://www.scielo.br/aabchttps://old.scielo.br/oai/scielo-oai.php||aabc@abc.org.br1678-26900001-3765opendoar:2007-03-23T00:00Anais da Academia Brasileira de Ciências (Online) - Academia Brasileira de Ciências (ABC)false
dc.title.none.fl_str_mv Finitely curved orbits of complex polynomial vector fields
title Finitely curved orbits of complex polynomial vector fields
spellingShingle Finitely curved orbits of complex polynomial vector fields
Mafra,Albetã C.
Holomorphic foliations
polynomial vector fields
algebraic curves
finite total curvature
title_short Finitely curved orbits of complex polynomial vector fields
title_full Finitely curved orbits of complex polynomial vector fields
title_fullStr Finitely curved orbits of complex polynomial vector fields
title_full_unstemmed Finitely curved orbits of complex polynomial vector fields
title_sort Finitely curved orbits of complex polynomial vector fields
author Mafra,Albetã C.
author_facet Mafra,Albetã C.
author_role author
dc.contributor.author.fl_str_mv Mafra,Albetã C.
dc.subject.por.fl_str_mv Holomorphic foliations
polynomial vector fields
algebraic curves
finite total curvature
topic Holomorphic foliations
polynomial vector fields
algebraic curves
finite total curvature
description This note is about the geometry of holomorphic foliations. Let X be a polynomial vector field with isolated singularities on C². We announce some results regarding two problems: 1. Given a finitely curved orbit L of X, under which conditions is L algebraic? 2. If X has some non-algebraic finitely curved orbit L what is the classification of X? Problem 1 is related to the following question: Let C <FONT FACE=Symbol>Ì</FONT> C² be a holomorphic curve which has finite total Gaussian curvature. IsC contained in an algebraic curve?
publishDate 2007
dc.date.none.fl_str_mv 2007-03-01
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=S0001-37652007000100002
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652007000100002
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/S0001-37652007000100002
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.79 n.1 2007
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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