论文标题
相关的参数理想力量紧密闭合过滤的渐变环
Associated graded rings of the filtration of tight closure of powers of parameter ideals
论文作者
论文摘要
让$ i $是一个在出色的Cohen-Macaulay本地域中的参数系统产生的理想。我们表明，相关的渐变环$ g^*（i）$ \ {（i^n）^*：n \ in \ mathbb {n} \} $是cohen-macaulay。我们证明，如果$ r $是一个很棒的布赫斯鲍姆本地领域，那么$ g^*（i）$是rees ring $ \ mathcal r^*（i）= \ oplus_ {n \ in \ mathbb {n}}（n}}}（i^n）（i^n）^*。过滤$ \ {（i^n）^*：in \ mathbb {n} \} $在出色的本地域中。证明中使用的重要工具是由于Hochster和C. huneke的深刻结果，它指出，出色的本地域的绝对积分封闭是一个很大的Cohen-Macaulay代数。我们计算$ i^n $的紧密关闭，其中$ i $是由均质的参数系统生成的，该系统在Hypersurface Ring $ r = \ Mathbb {f} _p [x_0，\ ldots，\ ldots，x_d]/（x_0^r++++\ cdots+x_d^r）中，在hypersurface ring $ r = \ mathbb {f} _p [x_0，\ ldots，x_0 Cohen-Macaulay。我们为REES代数$ \ Mathcal r^*（i）$提供$ r，d，e $的条件。
Let $I$ be an ideal generated by a system of parameters in an excellent Cohen-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 prove that if $R$ is an excellent Buchsbaum local domain then $G^*(I)$ is a Buchsbaum module over the Rees ring $\mathcal R^*(I)=\oplus_{n\in \mathbb{N}}(I^n)^*.$ We provide quick proofs of well-known results of I. Aberbach, Huneke-Itoh and Huneke-Hochster about the filtration $\{(I^n)^*: n\in \mathbb{N}\}$ in excellent local domains. An important tool used in the proofs is a deep result due to M. Hochster and C. Huneke which states that the absolute integral closure of an excellent local domain is a big Cohen-Macaulay algebra. We compute the tight closure of $I^n$ where $I$ is generated by homogeneous system of 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 prove that $G^*(I)$ is Cohen-Macaulay. We provide conditions on $r, d, e$ for the Rees algebra $\mathcal R^*(I)$ to be Cohen-Macaulay.
