Utilize este identificador para referenciar este registo:
http://hdl.handle.net/10451/3821
Título: | Legendrian varieties and quasi-ordinary hypersurfaces |
Autor: | Araújo, António Manuel Bandeira Barata Alves de, 1972- |
Orientador: | Neto, Orlando, 1960- |
Palavras-chave: | Espacos de moduli Geometria algébrica Limites (Matemática) Variedades (Matemática) Teses de doutoramento - 2011 |
Data de Defesa: | 2011 |
Resumo: | This thesis is a study of the Legendrian Varieties that are conormals of quasi-ordinary hypersurfaces. In the first chapter we study the analytic classification of the Legendrian curves that are the conormal of a plane curve with a single Puiseux pair. Let m,n be the set of Legendrian curves that are the conormal of a plane curve with a Puiseux pair (m, n), where g.c.d.(m, n) = 1 and m > 2n, with semigroup as generic as possible. We show that the quotient of m,n by the group of contact transformations is a Zariski open set of a weighted projective space. The main tool used in the proof of this theorem is a classification/construction theorem for contact transformation that has since proved useful in other instances. In the second chapter we calculate the limits of tangents of a quasi-ordinary hypersurface. In particular, we show that the set of limits of tangents is, in general, a topological invariant of the hypersurface. In the third chapter we prove a desingularization theorem for Legendrian hypersurfaces that are the conormal of a quasi-ordinary hypersurface. One of the main ingredients of the proof is the calculation of the limits of tangents achieved in chapter two. |
Descrição: | Tese de doutoramento, Matemática (Geometria e Topologia), Universidade de Lisboa, Faculdade de Ciências, 2011 |
URI: | http://hdl.handle.net/10451/3821 |
Aparece nas colecções: | FC - Teses de Doutoramento |
Ficheiros deste registo:
Ficheiro | Descrição | Tamanho | Formato | |
---|---|---|---|---|
ulsd61005_td_Antonio_Araujo.pdf | 1,11 MB | Adobe PDF | Ver/Abrir |
Todos os registos no repositório estão protegidos por leis de copyright, com todos os direitos reservados.