منابع مشابه
Rees Algebras of Diagonal Ideals
There is a natural epimorphism from the symmetric algebra to the Rees algebra of an ideal. When this epimorphism is an isomorphism, we say that the ideal is of linear type. Given two determinantal rings over a field, we consider the diagonal ideal, kernel of the multiplication map. We prove in many cases that the diagonal ideal is of linear type and recover the defining ideal of the Rees algebr...
متن کاملCohen-macaulayness of Rees Algebras of Diagonal Ideals
Given two determinantal rings over a field k, we consider the Rees algebra of the diagonal ideal, the kernel of the multiplication map. The special fiber ring of the diagonal ideal is the homogeneous coordinate ring of the secant variety. When the Rees algebra and the symmetric algebra coincide, we show that the Rees algebra is CohenMacaulay.
متن کاملCombinatorics of Symbolic Rees Algebras of Edge Ideals of Clutters
Let C be a clutter and let I be its edge ideal. We present a combinatorial description of the minimal generators of the symbolic Rees algebra Rs(I) of I . It is shown that the minimal generators of Rs(I) are in one to one correspondence with the irreducible parallelizations of C. From our description some major results on symbolic Rees algebras of perfect graphs and clutters will follow. As a b...
متن کاملLinks of prime ideals and their Rees algebras
In a previous paper we exhibited the somewhat surprising property that most direct links of prime ideals in Gorenstein rings are equimultiple ideals with reduction number 1. This led to the construction of large families of Cohen–Macaulay Rees algebras. The first goal of this paper is to extend this result to arbitrary Cohen–Macaulay rings. The means of the proof are changed since one cannot de...
متن کاملRees Algebras of Modules
We study Rees algebras of modules within a fairly general framework. We introduce an approach through the notion of Bourbaki ideals that allow the use of deformation theory. One can talk about the (essentially unique) Bourbaki ideal I(E) of a module E which, in many situations, allows to reduce the nature of the Rees algebra of E to that of its Bourbaki ideal I(E). Properties such as Cohen–Maca...
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ژورنال
عنوان ژورنال: Journal of Commutative Algebra
سال: 2013
ISSN: 1939-2346
DOI: 10.1216/jca-2013-5-3-359