Publicação
Legendrian varieties and quasi-ordinary hypersurfaces
| dc.contributor.advisor | Neto, Orlando, 1960- | por |
| dc.contributor.author | Araújo, António Manuel Bandeira Barata Alves de, 1972- | |
| dc.date.accessioned | 2011-07-26T17:13:10Z | |
| dc.date.available | 2011-07-26T17:13:10Z | |
| dc.date.issued | 2011 | |
| dc.description | Tese de doutoramento, Matemática (Geometria e Topologia), Universidade de Lisboa, Faculdade de Ciências, 2011 | por |
| dc.description.abstract | 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. | por |
| dc.description.sponsorship | Fundação para a Ciência e Tecnologia, Portugal, PRAXIS XXI/BD/15915/98. | por |
| dc.identifier.uri | http://hdl.handle.net/10451/3821 | |
| dc.language.iso | eng | por |
| dc.subject | Espacos de moduli | por |
| dc.subject | Geometria algébrica | por |
| dc.subject | Limites (Matemática) | por |
| dc.subject | Variedades (Matemática) | por |
| dc.subject | Teses de doutoramento - 2011 | por |
| dc.title | Legendrian varieties and quasi-ordinary hypersurfaces | por |
| dc.type | doctoral thesis | |
| dspace.entity.type | Publication | |
| rcaap.rights | openAccess | por |
| rcaap.type | doctoralThesis | por |