Poliedros de Newton e invariantes de singularidades determinantais
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...
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| Tipo de documento: | tese |
| Estado: | Versão publicada |
| Data de publicação: | 2024 |
| País: | Brasil |
| Recursos: | Universidade Federal de São Carlos (UFSCAR) |
| Repositório: | Repositório Institucional da UFSCAR |
| Idioma: | inglês |
| OAI Identifier: | oai:repositorio.ufscar.br:20.500.14289/19751 |
| Acesso em linha: | https://repositorio.ufscar.br/handle/20.500.14289/19751 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Singularidades Determinantais Obstrução de Euler Local Poliedros de Newton OSCAR Whitney Equisingularidade Determinantal Singularities Local Euler Obstruction Newton Polyhedra Whitney Equisingularity Determinantiellen Singularitäten Lokale Euler-Obstruktion Newton-Polyeder Whitney-Äquisingularität CIENCIAS EXATAS E DA TERRA::MATEMATICA |
| Resumo: | 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. |
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