特異点の環構造

奇点环结构

• 批准号: 08640067
• 负责人: 後藤 四郎
• 金额: $ 0.96万
• 依托单位: Meiji University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1996
• 资助国家: 日本
• 起止时间: 1996 至 无数据
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-08640067/
• 关键词: Gorenstein ring; Cohen-Macaulay ring; Rees algebra; associated graded ring; 不変部分環; minimal multipliciy

本研究の長期的な目標は特異点解消の代数的方法の開発にある。非特異化問題の難解さに鑑み、当面の課題を比較的容易であると予想されるCohen-Macaulay化など特異点を段階的に改良する理論的方法の開発に置く。基礎研究拡充のために、幾何学を専門領域とする服部・阿原と密接な連絡をとりつつ、Rees代数(blow-up rings)の環構造の研究を基本に、blowing-upを手法とする特異点改良の研究を行った。成果としては、Gorenstein局所環内の解析的差数1のイデアルに関しては、その随伴次数代数の環構造のGorenstein性について注目すべき知見が得られた(S.Goto,Y.Nakamura and K.Nishida,On the Goresteinness of graded rings associated to certain ideals of analytic deviation 1,to appear in Japan.J.Math.)。平行して一般的なCohen-Macaulay局所環内のイデアルに随伴する次数環のCohen-Macaulay性の研究を行い、納得すべき一般的な状況下で実際的な判定条件を記述するに至った(S.Goto,Y.Nakamura and K.Nishida,Cohen-Macaulayness in graded rings associated to ideals,J.Math.Kyoto Univ.,36(1996),229-250及びCohen-Macaulay graded rings associated to ideals,Amer.J.Math.,118(1996),1197-1213)ことは収穫である。他に、有限群をRees代数に作用させその不変部分環のCorenstein性を随伴次数環の不変部分環の言葉で簡潔に記述することに成功した(居相真一郎・後藤四郎:有限群のRees代数への作用とその不変部分環のGerenstein性について、明治大学科学技術研究所紀要,35(1996),59-70)のみでなく、minimal multiplicityを持つイデアルのRees代数のCohen-Macaulay性を解析し(S.Goto,S.-i.Iai,and Y.Nakamura,Cohen-Macaulayness versus the negativitiy of a-invariants in Rees algebras associated to ideals of minimal multiplicity to appear in Mem.Inst.Sci.&Tech,Meiji Univ.)、Rees代数のBuchsbaum性の研究に関する端緒(S.Goto,Buchsbaumness in Rees algebras associated to ideals of minimal multiplicity,Preprint 1996)を掴むことができたことは、大きな収穫であったと思われる。

The purpose of this study is to study the method of eliminating algebra by solving special points for a long time. Non-specific problems are easy to analyze and compare face-to-face problems. You want to use the improved theory of Cohen-Macaulay to improve the theory of special points. In the field of basic research, Hattori Ahara of Hattori, Rees Algebra (blow-up rings), basic research, blowing-up techniques, special point improvement, and so on. The results show that the difference in the analysis of the data in the local environment of the Gorenstein Bureau is as follows: 1. The difference in the analysis of the data in the environment of the Gorenstein Bureau is as follows: 1. The number of times that accompany the algebraic environment makes it possible to know the difference (S.Gotothine Y. Nakamura and K. Nishidaon on the Goresteinness of graded rings associated to certain ideals of analytic deviation 1 to appear in Japan.J.Math.). Parallel to the general situation in the Cohen-Macaulay office, the number of cases accompanied by the number of cases in the Cohen-Macaulay study, the general conditions for determining the number of cases, and the conditions for determining the performance of the international community were recorded in the context of the general situation (S.Gotomine Y.Nakamura and K. NishidaCohenmai Macaulayness in graded rings associated to ideals,J.Math.Kyoto Univ.,36 (1996), 229,250 and Cohen-Macaulay graded rings associated to ideals,Amer.J.Math.,118 (1996). 1197-1213) please do not know what to do. In other words, the role of Rees algebras in finite groups is not related to the number of times of Corenstein sex in the environment, and the number of times in the environment is not affected by the number of times in the environment. Goto Shiro, Meiji University Institute of Science and Technology 35 (1996) 59-70) the Cohen-Macaulay properties of Rees algebras were analyzed by minimal multiplicity and Buchsbaum algebras (S.GotoMagi. Iaifli and Y. Nakamura Macaulayness versus the negativitiy of a-invariants in Rees algebras associated to ideals of minimal multiplicity to appear in Mem.Inst.Sci.&Tech,Meiji Univ.), and the Buchsbaum properties of Nakamura algebras were studied. Preprint 1996) I don't know what to do. I don't know. I don't know.

项目成果

後藤四郎: "Cohen-Macaulayness versus the negativity of a-invariants in Rees algebras associated to ideals of minimal multiplicity" to appear in Memoirs of the Institute of Science and Technology,Meiji University.

后藤四郎：“Cohen-Macaulayness 与与最小多重性理想相关的里斯代数中 a-不变量的负性”出现在明治大学科学技术研究所回忆录中。

後藤四郎: "Cohen-Macaulayness ingraded rings associated to ideals." J. Math. Kyoto Univ. 36. 229-250 (1996)

Shiro Goto：“Cohen-Macaulayness 与理想相关的环。” J. Math. 36. 229-250 (1996)

後藤四郎: "Injective dimension in Noetherian algebras" Proceedings of the 29-th Symposium on Ring Theory and Representation Theory. 29. 7-16 (1997)

后藤四郎：“诺特代数中的内射维数”第 29 届环理论和表示论研讨会论文集 29. 7-16 (1997)。

後藤四郎: "On the Gorensteinness of graded rings associated to certain ideals of analytic deviation one" to appear in Japan.J.Math.

Shiro Goto：“论与分析偏差的某些理想相关的分级环的 Gorensteinness”，发表于 Japan.J.Math。

後藤四郎: "Cohen-Macaulay graded rings associated to ideals" Amer.J.Math.118. 1197-1213 (1996)

Shiro Goto：“Cohen-Macaulay 分级环与理想相关”Amer.J.Math.1197-1213 (1996)。