Topics on the Cohen-Macaulay Property of Rees Algebras and the Gorenstein Linkage Class of a Complete Intersection
Abstract
We study the Cohen-Macaulay property of Rees algebras of modules of K¨ahler differentials. When the module of differentials has projective dimension one, it is known that conditionF1 is sufficient for the Rees algebra to be Cohen-Macaulay. The converse was proved if the module of differentials is already F0. We weaken the condition F0globally by assuming some homogeneity condition. 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. 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.
Degree
Ph.D.
Advisors
Ulrich, Purdue University.
Subject Area
Mathematics
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