Study of blowing-aps.

吹气的研究。

• 批准号: 13640034
• 负责人: KAWASAKI Takeshi
• 金额: $ 2.37万
• 依托单位: Tokyo Metropolitan University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13640034/
• 关键词: Cohen-Macaulay ring; excellent ring; Rees algebra; dualzing complex; Cousin complex; Rees環; blowing-up; Cohen-Macaulay化; 正準加群; 双対化複体; cousin複体; スタンダード・パラメーター系; Noether環; 特異点解消

Let A be a Noetherian ring and I an ideal of A. If I is of positive height and the Rees algebra R(I) of I is Cohen-Macaulay, then R(I) is called an Arithmetic Cohen-Macaulayfication of A. We give a necessary and sufficient condition for A to have an arithmetic Macaulayfication. That is, A has an arithmetic Macaulayfication if and only if A satisfies(C1)A is universally catenary ;(C2)all the formal fiber of any localization of A are Cohen-Macaulay ;(C3)the Cohen-Macaulay locus of any finitely generated A-algebra B is open in Spec B ;(QU)for any pair of prime ideals p ⊂ q, ht q = ht q/p + ht p ;(UM)A has no embedded primes.In consequence of this result, we show that A is a homomorphic image of a Cohen-Macaulay ring if and only if A satisfies (C1)-(C3) and(CD)A has a codimension function.

设A是Noether环，I是A的理想.如果I是正高度的，且I的Rees代数R（I）是Cohen-Macaulay，则R（I）称为A的算术Cohen-Macaulay化。给出了A具有算术Macaulayization的一个充要条件。也就是说，A有算术Macaulay化当且仅当A满足（C1）A是泛悬链线，（C2）A的任何局部化的所有形式纤维都是Cohen-Macaulay，（C3）任何一个广义生成的A-代数B的Cohen-Macaulay轨迹在Spec B中是开的，（QU）对任何一对素理想p q，ht q = ht q/p + ht p ;（UM）A没有嵌入素数，由此证明了A是Cohen-Macaulay环的同态象当且仅当A满足（C1）-（C3）且（CD）A有余维数函数.

项目成果

Kawasaki, Takesi: "On arithmetic Macaulayfication of Noetherian rings"Trans.Amer.Math.Soc.. 123-149 (2002)

Kawasaki，Takesi：“论诺特环的算术麦考利化”Trans.Amer.Math.Soc.. 123-149 (2002)

K.kurano: "On Chow groups of G-graded rings"Comm. Algebra. 31. 2141-2160 (2003)

K.kurano：“On Chow 组 G 级戒指”Comm。

Terao, Hiroaki: "The Poincare series of the algebra of rational functions"J.Algebra. 266. 169-179 (2003)

Terao Hiroaki：“有理函数代数的庞加莱级数”J.Algebra。

K.Kurano: "Todd classes of affine cones of Grassmaunians"Int. Math. Res. Notices. 35. 1841-1855 (2002)

K.Kurano：“Grassmaunians 的仿射锥的托德类”Int。

Kawasaki, Takesi: "On arithmetic Cohen-Macaulayfication of Noetherian rings"Trans.Amer.Math.Soc.. 354. 123-149 (2002)

Kawasaki，Takesi：“论诺特环的算术 Cohen-Macaulayification”Trans.Amer.Math.Soc.. 354. 123-149 (2002)