Sylvester forms and Rees algebras

• Autor(a) principal: Macêdo, Ricado Burity croccia
• Data de Publicação: 2015
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da UFPB
• Texto Completo: https://repositorio.ufpb.br/jspui/handle/tede/8071
• topic: Algebra de Rees; Rees algebra; Numero de reducão; Formas de Sylvester; Funcão de Hilbert; Ideais iniciais; Quase Cohen-Macaulay; Mapping cone; Reduction number; CIENCIAS EXATAS E DA TERRA::MATEMATICA

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.