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Topics on the Cohen-Macaulay Property of Rees algebras and the Gorenstein linkage class of a complete intersectionTan T Dang (9183356) 30 July 2020 (has links)
We study the Cohen-Macaulay property of Rees algebras of modules of Kähler differentials. When the module of differentials has projective dimension one, it is known that condition $F_1$ is sufficient for the Rees algebra to be Cohen-Macaulay. The converse was proved if the module of differentials is already $F_0$. We weaken the condition $F_0$ globally by assuming some homogeneity condition.<br> <br> We are also interested in the defining ideal of the Rees algebra of a Jacobian module. If the Jacobian module is an ideal, we prove a formula for computing the defining ideal. Using the formula, we give an explicit description of the defining ideal in the monomial case. From there, we characterize the Cohen-Macaulay property of the Rees algebra.<br> <br> In the last chapter, we study Gorenstein linkage mostly in the graded case. In particular, we give an explicit example of a class of monomial ideals that are in the homogeneous Gorenstein linkage class of a complete intersection. To do so, we prove a Gorenstein double linkage construction that is analogous to Gorenstein biliaison.
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Fecho Integral de Módulos e Equisingularidade de Espaços Analíticos Complexos / Fecho Integral de Módulos e Equisingularidade de Espaços Analíticos ComplexosArruda, Rodrigo Alves de Oliveira 06 June 2008 (has links)
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Previous issue date: 2008-06-06 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Neste trabalho provamos o Teorema algebro-geométrico de Ganey, o qual
caracteriza completamente as condições de Whitney de famílias de espaços analíticos
complexos com singularidades arbitrárias em termos do fecho integral de módulos
naturalmente associados a estas famílias. / Neste trabalho provamos o Teorema algebro-geométrico de Ganey, o qual
caracteriza completamente as condições de Whitney de famílias de espaços analíticos
complexos com singularidades arbitrárias em termos do fecho integral de módulos
naturalmente associados a estas famílias.
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