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Topics on the Cohen-Macaulay Property of Rees algebras and the Gorenstein linkage class of a complete intersection

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.

  1. 10.25394/pgs.12735740.v1
Identiferoai:union.ndltd.org:purdue.edu/oai:figshare.com:article/12735740
Date30 July 2020
CreatorsTan T Dang (9183356)
Source SetsPurdue University
Detected LanguageEnglish
TypeText, Thesis
RightsCC BY 4.0
Relationhttps://figshare.com/articles/thesis/Topics_on_the_Cohen-Macaulay_Property_of_Rees_algebras_and_the_Gorenstein_linkage_class_of_a_complete_intersection/12735740

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