Convex foliations of degree 5 on the complex projective plane
We show that, up to automorphisms of P2C, there are fourteen homogeneous convex foliations of degree 5 on P2C. We establish some properties of the Fermat foliation F0d of degree d ≥ 2 and of the Hilbert modular foliation FH5 of degree 5. As a consequence, we obtain that every reduced convex foliatio...
| Autores: | , |
|---|---|
| Formato: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2021 |
| País: | España |
| Recursos: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2072/531299 |
| Acesso em linha: | http://hdl.handle.net/2072/531299 |
| Access Level: | acceso abierto |
| Palavra-chave: | Camacho–Sad index Convex foliation Homogeneous foliation Radial singularity 51 |
| Resumo: | We show that, up to automorphisms of P2C, there are fourteen homogeneous convex foliations of degree 5 on P2C. We establish some properties of the Fermat foliation F0d of degree d ≥ 2 and of the Hilbert modular foliation FH5 of degree 5. As a consequence, we obtain that every reduced convex foliation of degree 5 on P2C is linearly conjugated to one of the two foliations F05 or FH5 , which is a partial answer to a question posed in 2013 by D. Marín and J. V. Pereira. We end with two conjectures about the Camacho–Sad indices along the line at infinity at the non radial singularities of the homogeneous convex foliations of degree d ≥ 2 on P2C © 2021 Universitat Autonoma de Barcelona. All rights reserved. |
|---|