Submitted by Maike Costa (maiksebas@gmail.com) on 2016-03-31T12:43:01Z No. of bitstreams: 1 arquivo total.pdf: 1366177 bytes, checksum: 1b02d1a5ce5861390070022558e311b0 (MD5) / Made available in DSpace on 2016-03-31T12:43:01Z (GMT). No. of bitstreams: 1 arquivo total.pdf: 1366177 bytes, checksum: 1b02d1a5ce5861390070022558e311b0 (MD5) Previous issue date: 2015-07-24 / This work is about the Rees algebra of a nite colength almost complete intersection ideal generated by forms of the same degree in a polynomial ring over a eld. We deal with two situations which are quite apart from each other: in the rst the forms are monomials in an unrestricted number of variables, while the second is for general binary forms. The essential goal in both cases is to obtain the depth of the Rees algebra. It is known that for such ideals the latter is rarely Cohen{Macaulay (i.e., of maximal depth). Thus, the question remains as to how far one is from the Cohen{Macaulay case. In the case of monomials one proves under certain restriction a conjecture of Vasconcelos to the e ect that the Rees algebra is almost Cohen{ Macaulay. At the other end of the spectrum, one proposes a proof of a conjecture of Simis on general binary forms, based on work of Huckaba{Marley and on a theorem concerning the Ratli {Rush ltration. Still within this frame, one states a couple of stronger conjectures that imply Simis conjecture, along with some solid evidence. / Este trabalho versa sobre a algebra de Rees de um ideal quase intersec cão completa, de cocomprimento nito, gerado por formas de mesmo grau em um anel de polinômios sobre um corpo. Considera-se duas situa c~oes inteiramente diversas: na primeira, as formas s~ao mon^omios em um n umero qualquer de vari aveis, enquanto na segunda, s~ao formas bin arias gerais. O objetivo essencial em ambos os casos e obter a profundidade da algebra de Rees. E conhecido que tal algebra e raramente Cohen{Macaulay (isto e, de profundidade m axima). Assim, a quest~ao que permanece e qua o distante são do caso Cohen{Macaulay. No caso de monômios prova-se, mediante certa restri cão, uma conjectura de Vasconcelos no sentido de que a algébra de Rees e quase Cohen {Macaulay. No outro caso extremo, estabelece-se uma prova de uma conjectura de Simis sobre formas bin arias gerais, baseada no trabalho de Huckaba{Marley e em um teorema sobre a ltera cão de Ratli {Rush. Al em disso, apresenta-se um par de conjecturas mais fortes que implicam a conjectura de Simis, juntamente com uma evidência s olida.