English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Let $I$ be an ideal generated by a system of parameters in an excellentCohen-Macaulay local domain. We show that the associated graded ring $G^*(I)$of the filtration $\{(I^n)^*: n\in \mathbb{N}\}$ is Cohen-Macaulay. We provethat if $R$ is an excellent Buchsbaum local domain then $G^*(I)$ is a Buchsbaummodule over the Rees ring $\mathcal R^*(I)=\oplus_{n\in \mathbb{N}}(I^n)^*.$ Weprovide quick proofs of well-known results of I. Aberbach, Huneke-Itoh andHuneke-Hochster about the filtration $\{(I^n)^*: n\in \mathbb{N}\}$ inexcellent local domains. An important tool used in the proofs is a deep resultdue to M. Hochster and C. Huneke which states that the absolute integralclosure of an excellent local domain is a big Cohen-Macaulay algebra. Wecompute the tight closure of $I^n$ where $I$ is generated by homogeneous systemof parameters having the same degree $e$ in the hypersurface ring$R=\mathbb{F}_p[X_0,\ldots ,X_d]/(X_0^r+\cdots+X_d^r).$ In such cases we provethat $G^*(I)$ is Cohen-Macaulay. We provide conditions on $r, d, e$ for theRees algebra $\mathcal R^*(I)$ to be Cohen-Macaulay.

Associated graded rings of the filtration of tight closure of powers of parameter ideals