| Project/Area Number |
13640034
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Tokyo Metropolitan University |
|---|
Principal Investigator |
KAWASAKI Takeshi Tokyo Metropolitan University, Graduate School of Science, assistant, 理学研究科, 助手 (40301410)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
TERAO Hiroaki Tokyo Metropolitan University, Graduate School of Science, professor, 理学研究科, 教授 (90119058)
KURANO Kazuhiko Meiji University, school of soi. and teohv, professor, 理工学部, 教授 (90205188)
|
|---|
| Project Period (FY) |
2001 – 2003
|
| Project Status |
Completed (Fiscal Year 2003)
|
| Budget Amount *help |
¥3,700,000 (Direct Cost: ¥3,700,000)
Fiscal Year 2003: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2002: ¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 2001: ¥1,300,000 (Direct Cost: ¥1,300,000)
|
|---|
| Keywords | 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 |
|---|
| Research Abstract |
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.
|
