On the Cohen-Macaulayness of multi-Rees algebras and Rees algebras of powers of ideals
نویسندگان
چکیده
منابع مشابه
Cohen-macaulayness of Rees Algebras of Modules
We provide the sufficient conditions for Rees algebras of modules to be Cohen-Macaulay, which has been proven in the case of Rees algebras of ideals in [11] and [4]. As it turns out the generalization from ideals to modules is not just a routine generalization, but requires a great deal of technical development. We use the technique of generic Bourbaki ideals introduced by Simis, Ulrich and Vas...
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 کاملRees 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-Macaulay Rees Algebras and Their Specialization
an isomorphism? These questions have interest partly because if S and .S’(J, S) are Cohen-Macaulay, then so is gr, S := S/J@ J/J’... [ 16 1 and under these hypotheses if N is perfect and R @ .S(J, S) = .$(I, R), then R and .7(1. R) are Cohen-Macaulay too. Thus, gr,R is Cohen-Macaulay, and its torsion freeness and normality, for exmple, can be characterized in terms of analytic spreads, as in [ ...
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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the Mathematical Society of Japan
سال: 1998
ISSN: 0025-5645
DOI: 10.2969/jmsj/05020451