| Journal: | Boletín de la Sociedad Matemática Mexicana |
| Database: | PERIÓDICA |
| System number: | 000345590 |
| ISSN: | 0037-8615 |
| Authors: | Alcántara, Claudia R1 |
| Institutions: | 1Universidad de Guanajuato, Departamento de Matemáticas, Guanajuato. México |
| Year: | 2010 |
| Season: | Abr |
| Volumen: | 16 |
| Number: | 1 |
| Pages: | 39-52 |
| Country: | México |
| Language: | Inglés |
| Document type: | Artículo |
| Approach: | Experimental, analítico |
| English abstract | Let Fd be the space of holomorphic foliations of CP of degree d. We study the linear action PGL(3,C)×Fd → Fd given by gX = DgX ◦ (g−1) in the sense of Mumford in [3]. In this paper we prove that an unstable foliation X of degree d ≥ 2 satisfies one of the following conditions: it is a Riccati foliation, or its automorphism group Aut(X) is finite abelian or it is isomorphic to a transitive finite subgroup of GL(2,C). We also prove the existence of degenerate singularities for unstable foliations; and we give a characterization of foliations on CP with an infinite automorphism group |
| Disciplines: | Matemáticas |
| Keyword: | Matemáticas puras, Geometría algebraica, Foliaciones holomórficas, Foliación de Riccati, Grupo de automorfismos |
| Keyword: | Mathematics, Pure mathematics, Algebraic geometry, Holomorphic foliations, Riccati foliation, Automorphism group |
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