Foliations with isolated singularities on Hirzebruch surfaces
[EN] We study foliations F on Hirzebruch surfaces Sd and prove that, similarly to those on the projective plane, any F can be represented by a bi-homogeneous polynomial affine 1-form. In case F has isolated singularities, we show that, for delta = 1, the singular scheme of F does determine the folia...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/183574 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/183574 |
| Access Level: | acceso abierto |
| Palabra clave: | Foliations on surfaces Singularities MATEMATICA APLICADA |
| Sumario: | [EN] We study foliations F on Hirzebruch surfaces Sd and prove that, similarly to those on the projective plane, any F can be represented by a bi-homogeneous polynomial affine 1-form. In case F has isolated singularities, we show that, for delta = 1, the singular scheme of F does determine the foliation, with some exceptions that we describe, as is the case of foliations in the projective plane. For delta not equal 1, we prove that the singular scheme of F does not determine the foliation. However, we prove that, in most cases, two foliations F and F' given by sections s and s' have the same singular scheme if and only if s' = Phi(s), for some global endomorphism F of the tangent bundle of S-delta. |
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