2022 Fiscal Year Final Research Report
Reinterpretation of GIT from the view point of Lie algebras and its applications
Project/Area Number |
20K03526
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Multi-year Fund |
Section | 一般 |
Review Section |
Basic Section 11010:Algebra-related
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Research Institution | Fukushima National College of Technology |
Principal Investigator |
Sawada Tadakazu 福島工業高等専門学校, 一般教科, 准教授 (80647438)
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Project Period (FY) |
2020-04-01 – 2023-03-31
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Keywords | フロベニウス・サンドイッチ |
Outline of Final Research Achievements |
A set on which addition, subtraction, multiplication, and division are defined is called a field. Complex numbers C form a field and any non-constant polynomial with coefficients in C has a root in C. Such a field is called an algebraically closed field. The characteristic of a field is defined to be the smallest positive integer n such that n1=0. We construct a projective plane by adding a line at infinity of the Euclidian plane. The notion of 1-foliations is defined on the projective plane, and the quotient of the projective plane by a 1-foliation is deduced naturally. We classify the configurations of the singular points which appear on the quotients of the projective plane by the 1-foliations of degree -1 in characteristic 2.
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Free Research Field |
代数幾何学
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Academic Significance and Societal Importance of the Research Achievements |
数学は現代社会の基礎を支えるものであり、その理論の整備は社会の発展に不可欠である。ただ、数学のどの理論がどのタイミングでどのように具体的に応用されるか予測することは困難であり、だからこそ、将来の未知の応用に向けて基礎理論をしっかりと構築しておくことが大切である。本研究では数学の一分野である代数幾何学において、射影平面の商に現れる特異点の配置について分類を行った。本研究は点の配置問題としての側面もあり、純粋数学の理論としての意義に加え、原子の配置問題などの現実的な応用への備えとしても意義のあるものだと考えられる。
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