Research on Noetherian property of symbolic Rees algebras

2014 Fiscal Year Final Research Report

• Project/Area Number: 23540042
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Chiba University
• Principal Investigator: NISHIDA Koji 千葉大学, 統合情報センター, 教授 (60228187)
• Co-Investigator(Renkei-kenkyūsha): KURANO Kazuhiko 明治大学, 理工学研究科, 教授 (90205188)
• Research Collaborator: FUKUMURO Kosuke ; INAGAWA Taro
• Project Period (FY): 2011-04-28 – 2015-03-31
• Keywords: 可換環 / 記号的べき乗 / 記号的リース代数

Outline of Final Research Achievements

In this research, we aimed to find a new method for computing symbolic powers of ideals in 3-dimensional regular local (or polynomial) rings. Furthermore, we aimed to improve the Huneke's criterion for symbolic Rees algebras to be Noethrian.
In the first year, using *-transform of acyclic complexes, we found a specific procedure to induce free resolutions of symbolic powers from those of ordinary powers. Next year, we gave a new criterion on the Noetherian property of symbolic Rees algebras. In the third year, we checked the practicality of the results we found in the last two years by applying them to concrete examples. The last year was devoted for extending the class of ideals whose symbolic Rees algebras are not Noetherian.

Free Research Field

可換環論