Hilbert coefficients and the associated graded rings
نویسندگان
چکیده
منابع مشابه
Depth of Associated Graded Rings via Hilbert Coefficients of Ideals
Given a local Cohen-Macaulay ring (R,m), we study the interplay between the integral closedness – or even the normality – of an m-primary R-ideal I and conditions on the Hilbert coefficients of I . We relate these properties to the depth of the associated graded ring of I .
متن کاملHilbert Coefficients and Depths of Form Rings
We present short and elementary proofs of two theorems of Huckaba and Marley, while generalizing them at the same time to the case of a module. The theorems concern a characterization of the depth of the associated graded ring of a Cohen-Macaulay module, with respect to a Hilbert filtration, in terms of the Hilbert coefficient e1. As an application, we derive bounds on the higher Hilbert coeffi...
متن کاملHilbert Coefficients and Depth of the Associated Graded Ring of an Ideal
In this expository paper we survey results proved during the last fifty years that relate Hilbert coefficients e0(I) and e1(I) of an m-primary ideal I in a Cohen-Macaulay local ring (R, m) with depth of the associated graded ring G(I). Several results in this area follow from two theorems of S. Huckaba and T. Marley. These were proved using homological techniques. We provide simple proofs using...
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According to a theorem of Monsky, the Hilbert–Kunz function of a 1-dimensional standard graded algebra R over a finite field K has, for i 0, the shape HKR(i) = c(R) · p i + φ(i), where c(R) is the multiplicity of R and φ is a periodic function. Here we study explicit computer algebra algorithms for computing such Hilbert–Kunz functions: the period length and the values of φ, as well as a concre...
متن کاملSally Modules and Associated Graded Rings
To frame and motivate the goals pursued in the present article we recall that, loosely speaking, the most common among the blowup algebras are the Rees algebra R[It] = ⊕∞ n=0 I ntn and the associated graded ring grI(R) = ⊕∞ n=0 I n/In+1 of an ideal I in a commutative Noetherian local ring (R,m). The three main clusters around which most of the current research on blowup algebras has been develo...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1999
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-99-05080-7