Submitted by Maike Costa (maiksebas@gmail.com) on 2016-03-31T13:40:38Z No. of bitstreams: 1 arquivo total.pdf: 1581712 bytes, checksum: 55cfc2e330d11ed8545538014daa3873 (MD5) / Made available in DSpace on 2016-03-31T13:40:38Z (GMT). No. of bitstreams: 1 arquivo total.pdf: 1581712 bytes, checksum: 55cfc2e330d11ed8545538014daa3873 (MD5) Previous issue date: 2015-07-16 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / 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. / Nesta disserta c~ao, inicialmente apresentamos no c~oes gerais sobre a algebra sim etrica e a algebra de Rees no contexto amplo de m odulos, e consideramos particularmente a situa c~ao especial na qual o dado m odulo possui apresenta c~ao linear. Na sequ^encia, o principal objetivo e o estudo de tais algebras de blowup no caso em que o m odulo e o celebrado m odulo de diferenciais de K ahler, tendo como foco a investiga c~ao de uma interessante vers~ao da persistente Conjectura de Berger para a algebra sim etrica, bem como o estudo de propriedades fundamentais como: integridade, Cohen-Macaulicidade e normalidade; tais propriedades s~ao tamb em investigadas de forma especial no caso da algebra de Rees (do m odulo de diferenciais), evidenciando inclusive a conex~ao com as chamadas condi c~oes de Fitting.