Álgebras simétrica e de Rees do módulo de diferenciais de Kähler

• Autor(a) principal: Sousa, Fraciélia Limeira de
• Data de Publicação: 2015
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da UFPB
• Texto Completo: https://repositorio.ufpb.br/jspui/handle/tede/8073
• topic: Algebra Simetrica; Symmetric Algebra; Algebra de Rees; Módulo de diferenciais de Kahler; Rees Algebra; Module of Kahler Dierentials; CIENCIAS EXATAS E DA TERRA::MATEMATICA

In this dissertation, we initially present an overview about the symmetric and the Rees algebras in the wide context of modules, and we consider particularly the special situation in which the given module possesses a linear presentation. In the sequel, the main goal is the study of such blowup algebras in the case where the module is the celebrated module of K ahler di erentials, the focus being given on the investigation of an interesting version of the long-standing Berger's Conjecture for the symmetric algebra, as well as on the study of fundamental properties such as: integrality, Cohen- Macaulayness and normality; these properties are also investigated in a special way in the case of the Rees algebra (of the di erential module), highlighting the connection to the so-called Fitting conditions.