Repositório da Universidade de Lisboa >
Faculdade de Ciências (FC) >
FC - Teses de Doutoramento >
Please use this identifier to cite or link to this item:
|Title: ||Legendrian varieties and quasi-ordinary hypersurfaces|
|Authors: ||Araújo, António Manuel Bandeira Barata Alves de, 1972-|
|Advisor: ||Neto, Orlando, 1960-|
|Keywords: ||Espacos de moduli|
Teses de doutoramento - 2011
|Issue Date: ||2011|
|Abstract: ||This thesis is a study of the Legendrian Varieties that are conormals of
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
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.|
|Description: ||Tese de doutoramento, Matemática (Geometria e Topologia), Universidade de Lisboa, Faculdade de Ciências, 2011|
|Appears in Collections:||FC - Teses de Doutoramento|
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.