The classification of noncommutative algebraic surfaces using algebraic geometry and representation theory

2019 Fiscal Year Final Research Report

• Project/Area Number: 16K05097
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Shizuoka University
• Principal Investigator: Mori Izuru 静岡大学, 理学部, 教授 (50436903)
• Project Period (FY): 2016-04-01 – 2020-03-31
• Keywords: 環論 / 非可換代数幾何学 / 非可換射影空間 / 非可換射影曲面

Outline of Final Research Achievements

My research field is noncommutative algebraic geometry. I have focused on homological properties and classification of AS-regular algebras, which are homogeneous coordinate rings of noncommutative projective spaces, and on geometric properties and classification of noncommutative ruled surfaces. In this research project, I made the progress on the classification of 3-dimensional AS-regular algebras, the categorical characterization of noncommutative projective spaces, and the classification of noncommutative hypersurfaces and noncommutative ruled surfaces, using techniques of algebraic geometry and representation theory of algebras.

Free Research Field

非可換代数幾何学

Academic Significance and Societal Importance of the Research Achievements

非可換代数多様体の分類問題は、非可換代数幾何学の分野創設当初からの重要な研究課題であり、特に非可換射影空間や非可換射影曲面の分類問題は、現在にいたるまで欧米を中心として活発に研究されています。そのような状況の中この研究課題の成果はこれらの分類問題を大きく進展させたという意味で、学術的意義は大変高いものと考えられます。