Sobre o grau de componentes dos espaços das folheações holomorfas de codimensão um em CPn
Two of the main discrete invariants of a projective variety are its dimension and degree. The spaces of holomorphic foliations of codimension one and degree d in CPn, n 3 are subschemes of the projective space CP (H0(Pn; 1(d + 1))) defined by the equations ofconditon of integrability, w ^ dw = 0. We...
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| Tipo de recurso: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 2015 |
| País: | Brasil |
| Institución: | Universidade Federal de Minas Gerais (UFMG) |
| Repositorio: | Repositório Institucional da UFMG |
| Idioma: | portugués |
| OAI Identifier: | oai:repositorio.ufmg.br:1843/EABA-9UJRHB |
| Acceso en línea: | http://hdl.handle.net/1843/EABA-9UJRHB |
| Access Level: | acceso abierto |
| Palabra clave: | Matemática Folheações (Matematica) Aplicações holomorfas Geometria algebrica |
| Sumario: | Two of the main discrete invariants of a projective variety are its dimension and degree. The spaces of holomorphic foliations of codimension one and degree d in CPn, n 3 are subschemes of the projective space CP (H0(Pn; 1(d + 1))) defined by the equations ofconditon of integrability, w ^ dw = 0. We determine in this thesis the degrees of certain components of the spaces of holomorphicfoliations of codimension one in CPn, n 3. For each integer r 1, letR(2; 2r +1) denote the set of foliations induced by 1-forms of type 2FdG(2r +1)GdF, where F;G denote homogeneous polinomials of degrees 2; 2r + 1. X. Gomez-Mont e A. Lins Neto proved in [2] that R(2; 2r + 1) is an irreducible component of the space of holomorphic foliations of degree 2r + 1. After, J. V. Pereira, F. Cukierman and I. Vainsencher proved in [5] that it is a rational and generically reduced component. They found the degree of that component for r = 1; n 5 and conjectured a few more in higherdimensions.Our main result gives a closed formula for the degree of the component R(2; 2r + 1) for r 1 in arbitrary dimension n 2, to wit |
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