Deformations of legendrian curves

Bibliographic Details
Main Author: Silva Mendes, Marco
Publication Date: 2018
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: http://hdl.handle.net/10451/38260
Summary: Tese de doutoramento, Matemática (Geometria e Topologia), Universidade de Lisboa, Faculdade de Ciências, 2018
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spelling Deformations of legendrian curvesTeses de doutoramento - 2018Domínio/Área Científica::Ciências Naturais::MatemáticasTese de doutoramento, Matemática (Geometria e Topologia), Universidade de Lisboa, Faculdade de Ciências, 2018In chapters 1 and 2 we study deformations of Legendrian curves in P*C². In chapter 1 we construct versal and semiuniversal objects in the category of deformations of the parametrization of a germ of a Legendrian curve as well as in the subcategory of equimultiple deformations. We show that these objects are given by the conormal or fake conormal of an hypersurface in C² x Cʳ. In chapter 2 we prove the existence of equisingular versal and semiuniversal deformations of a Legendrian curve, on this instance making use of deformations of the equation. By equisingular we mean that the plane projection of the fibres have fixed topological type. We prove in particular that the base space of such an equisingular versal deformation is smooth and construct it explicitly when the special fibre has semiquasihomogeneous or Newton non-degenerate plane projection. Chapter 3 concerns the construction of a moduli space for Legendrian curves singularities which are contactomorphic-equivalent and equisingular through a contact analogue of the Kodaira-Spencer map for curve singularities. We focus on the specific case of Legendrian curves which are the conormal of a plane curve with one Puiseux pair. To do so, it is fundamental to understand how deformations of such singularities behave, which was done in the previous chapter. The equisingular semiuniversal microlocal deformations constructed in chapter 2 already contain in their base space all the relevant fibres in the construction of such a moduli space. This is so because all deformations are isomorphic through a contact transformation to the pull-back of a semiuniversal deformation.Neto, Orlando, 1960-Repositório da Universidade de LisboaSilva Mendes, Marco2019-05-17T11:06:41Z201820182018-01-01T00:00:00Zdoctoral thesisinfo:eu-repo/semantics/publishedVersionapplication/pdfhttp://hdl.handle.net/10451/38260TID:101304811enginfo:eu-repo/semantics/openAccessreponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2025-03-17T14:06:45Zoai:repositorio.ulisboa.pt:10451/38260Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-29T03:02:49.972347Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
dc.title.none.fl_str_mv Deformations of legendrian curves
title Deformations of legendrian curves
spellingShingle Deformations of legendrian curves
Silva Mendes, Marco
Teses de doutoramento - 2018
Domínio/Área Científica::Ciências Naturais::Matemáticas
title_short Deformations of legendrian curves
title_full Deformations of legendrian curves
title_fullStr Deformations of legendrian curves
title_full_unstemmed Deformations of legendrian curves
title_sort Deformations of legendrian curves
author Silva Mendes, Marco
author_facet Silva Mendes, Marco
author_role author
dc.contributor.none.fl_str_mv Neto, Orlando, 1960-
Repositório da Universidade de Lisboa
dc.contributor.author.fl_str_mv Silva Mendes, Marco
dc.subject.por.fl_str_mv Teses de doutoramento - 2018
Domínio/Área Científica::Ciências Naturais::Matemáticas
topic Teses de doutoramento - 2018
Domínio/Área Científica::Ciências Naturais::Matemáticas
description Tese de doutoramento, Matemática (Geometria e Topologia), Universidade de Lisboa, Faculdade de Ciências, 2018
publishDate 2018
dc.date.none.fl_str_mv 2018
2018
2018-01-01T00:00:00Z
2019-05-17T11:06:41Z
dc.type.driver.fl_str_mv doctoral thesis
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10451/38260
TID:101304811
url http://hdl.handle.net/10451/38260
identifier_str_mv TID:101304811
dc.language.iso.fl_str_mv eng
language eng
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron:RCAAP
instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron_str RCAAP
institution RCAAP
reponame_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository.name.fl_str_mv Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
repository.mail.fl_str_mv info@rcaap.pt
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