Hilbert function of local rings

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K04820
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Yamaguchi University
• Principal Investigator: Ozeki Kazuho 山口大学, 大学院創成科学研究科, 准教授 (70445849)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: ヒルベルト函数 / ヒルベルト係数 / Rees代数 / 随伴次数環 / Sally加群 / コーエン・マコ―レイ局所環

Outline of Final Research Achievements

The purpose of this research is to explore the behavior of the Hilbert functions　of ideals in Cohen-Macaulay local rings.
I explored the relationship between the first Hilbert coefficient and the structure of the associated graded ring of integrally closed ideals in a Cohen-Macaulay local ring.
I also gave a characterization for the almost minimal value of the first Hilbert coefficient in the case of the normal filtration in an analytically unramified Cohen-Macaulay local ring. I strongly used some structure theorems of Sally modules in these results.

Free Research Field

可換環論