Finitely curved orbits of complex polynomial vector fields
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| Natura: | Artículo científico |
| Lingua: | en |
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Academia Brasileira de Ciências
2007
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| _version_ | 1876436872752791552 |
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| author | Albetã C. Mafra |
| author_facet | Albetã C. Mafra |
| contents | Finitely curved orbits of complex polynomial vector fields Albetã C. Mafra Multidisciplinaria (Ciencias Naturales y Exactas) algebraic curves Holomorphic foliations finite total curvature polynomial vector fields This note is about the geometry of holomorphic foliations. Let X be a polynomial vectorfield with isolatedsingularities on C2. We announce some results regarding two problems: 1. Given a finitely curved orbit Lof X, under which conditions is L algebraic? 2. If X has some non-algebraic finitely curved orbit L whatis the classification of X? Problem 1 is related to the following question: LetC ⊂ C2 be a holomorphiccurve which has finite total Gaussian curvature. IsC contained in an algebraic curve? 2007 artículo científico 0001-3765 https://www.redalyc.org/articulo.oa?id=32779102 en http://www.redalyc.org/revista.oa?id=327 Anais da Academia Brasileira de Ciências application/pdf Academia Brasileira de Ciências Anais da Academia Brasileira de Ciências (Brasil) Num.1 Vol.79 |
| format | Artículo científico |
| id | redalyc_32779102 |
| institution | Redalyc |
| language | en |
| publishDate | 2007 |
| publisher | Academia Brasileira de Ciências |
| spellingShingle | Finitely curved orbits of complex polynomial vector fields Albetã C. Mafra Multidisciplinaria (Ciencias Naturales y Exactas) algebraic curves Holomorphic foliations finite total curvature polynomial vector fields Finitely curved orbits of complex polynomial vector fields Albetã C. Mafra Multidisciplinaria (Ciencias Naturales y Exactas) algebraic curves Holomorphic foliations finite total curvature polynomial vector fields This note is about the geometry of holomorphic foliations. Let X be a polynomial vectorfield with isolatedsingularities on C2. We announce some results regarding two problems: 1. Given a finitely curved orbit Lof X, under which conditions is L algebraic? 2. If X has some non-algebraic finitely curved orbit L whatis the classification of X? Problem 1 is related to the following question: LetC ⊂ C2 be a holomorphiccurve which has finite total Gaussian curvature. IsC contained in an algebraic curve? 2007 artículo científico 0001-3765 https://www.redalyc.org/articulo.oa?id=32779102 en http://www.redalyc.org/revista.oa?id=327 Anais da Academia Brasileira de Ciências application/pdf Academia Brasileira de Ciências Anais da Academia Brasileira de Ciências (Brasil) Num.1 Vol.79 |
| title | Finitely curved orbits of complex polynomial vector fields |
| topic | Multidisciplinaria (Ciencias Naturales y Exactas) algebraic curves Holomorphic foliations finite total curvature polynomial vector fields |
| url | https://www.redalyc.org/articulo.oa?id=32779102 |