Bi-Lipschitz invariant geometry

• Ano de defesa: 2018
• Autor(a) principal: Silva, Thiago Filipe da
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Bi-Lipschitz equisingularity; Determinantal varieties; Double of a module; Equisingularidade bi-Lipschitz; Fecho Integral de ideais e módulos; Integral closure of ideals and modules; Lipschitz saturation of a module; O double de um módulo; Saturação Lipschitz de um módulo; Variedades Determinantais
• Link de acesso: http://www.teses.usp.br/teses/disponiveis/55/55135/tde-05022018-141238/

The study about bi-Lipschitz equisingularity has been a very important subject in Singularity Theory in last decades. Many different approach have cooperated for a better understanding about. One can see that the bi-Lipschitz geometry is able to detect large local changes in curvature more accurately than other kinds of equisingularity. The aim of this thesis is to investigate the bi-Lipschitz geometry in an algebraic viewpoint. We define some algebraic tools developing classical properties. From these tools, we obtain algebraic criterions for the bi-Lipschitz equisingularity of some families of analytic varieties. We present a categorical and homological viewpoints of these algebraic structure developed before. Finally, we approach algebraically the bi-Lipschitz equisingularity of a family of Essentially Isolated Determinantal Singularities.