Poliedros de Newton e invariantes de singularidades determinantais

• Ano de defesa: 2024
• Autor(a) principal: Costa, Maicom Douglas Varella Costa
• Orientador(a): Hartmann Junior, Luiz Roberto
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Universidade Federal de São Carlos; Câmpus São Carlos
• Programa de Pós-Graduação: Programa de Pós-Graduação em Matemática - PPGM
• Palavras-chave em Português: Singularidades Determinantais; Obstrução de Euler Local; Poliedros de Newton; OSCAR
• Palavras-chave em Inglês: Whitney Equisingularidade; Determinantal Singularities; Local Euler Obstruction; Newton Polyhedra; Whitney Equisingularity
• Área do conhecimento CNPq: CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://repositorio.ufscar.br/handle/20.500.14289/19751

In this work, we study invariants of determinantal singularities, by analysing the Newton polyhedra which arise from the entries of a given matrix. The main contribution of this work is providing sufficient conditions, which guarantee the Whitney equisingularity of a family of isolated determinantal singularities (IDS) in terms of Newton polyhedra. We also introduce a formula to compute the local Euler obstruction of IDS in terms of Newton polyhedra and we simplify this formula for some classes of singularities, which must satisfy a condition on its Newton polyhedra. Lastly, we present an implementation on the software OSCAR in order to compute relative mixed volumes of pairs of polyhedra, to verify the non-degeneracy of a 2x3 matrix and to compute the local Euler obstruction of an IDS defined by a 2x3 matrix.