Sobre distribuição e folheações holomorfas de codimensão maior do que um
Let w be a holomorphic LDS r-form on a complex manifold M. In the case M = Cn, we show that if ker(w) admits a trivial subbundle of rank k, then there exists a holomrphic LDS (r - k)-form n on Cn such that ! is the exterior product of k with the product of k linearly independent global sections of k...
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| Tipo de recurso: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 2010 |
| País: | Brasil |
| Institución: | Universidade Federal de Minas Gerais (UFMG) |
| Repositorio: | Repositório Institucional da UFMG |
| Idioma: | portugués |
| OAI Identifier: | oai:repositorio.ufmg.br:1843/EABA-8CYHUK |
| Acceso en línea: | http://hdl.handle.net/1843/EABA-8CYHUK |
| Access Level: | acceso abierto |
| Palabra clave: | Codimensão Folheações holomorfas Matemática Folheações (Matematica) Funções holomorficas |
| Sumario: | Let w be a holomorphic LDS r-form on a complex manifold M. In the case M = Cn, we show that if ker(w) admits a trivial subbundle of rank k, then there exists a holomrphic LDS (r - k)-form n on Cn such that ! is the exterior product of k with the product of k linearly independent global sections of ker(w). In the case that M is compact and connected we approach the classical Darboux-Jouanolou problem and we prove that if w has a suficiently large number of invariant analytic hypersurfaces, then w admits a meromorphic first integral. Next, we prove that if k >= r and w has k infinite families of w-invariant analytic hypersurfaces whose members intersect transversely, then w admits a meromorphic first integral of rank k. In particular, if k = r, thenw! is integrable. Continuing in this direction we prove that in the integrable case ! has a transversal structure by translations if and only if w is a multiples of a product of closed 1-forms. We conclude this work by showing that in the presence of a Kupka type singularity, there exists a coordinate system around the singularity such that w reduces to r+1 variables. In particular, w is integrable and the foliation induced by w has the product struture of a foliation by curves in Cr+1 multiplied by a regular foliation. |
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