| Project/Area Number |
15K04872
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Nagoya Institute of Technology |
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Principal Investigator |
Minami Norihiko 名古屋工業大学, 工学(系)研究科(研究院), 教授 (80166090)
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| Project Period (FY) |
2015-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 代数幾何 / モチビックホモトピー論 / ホモトピー論 / 高次単線織性 / 高次ファノ多様体 / 有理多様体 / 単織多様体 / A1ホモトピー論 / ボット塔 / isogeny / 無限ループ空間 / ファノ多様体 / iso geny / 無隈ループ空間 / モチピックホモ卜ピー論 / 多重ゼータ値 / 場の量子論 |
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| Outline of Final Research Achievements |
Classical (stable) homotopy theory is now known to be subsumed by the Morel-Voevodsky A1-(stable)homotopy theory, which originates in algebraic geometr, which deals with common zeros of polynomials and polynomial maps between them. In search of some hierachy structure in the algebr-geometrically origined A1-(stable)homotopy theory, such as the Hopkins-Smith hierachy structure in the classical (stable) homotopy theory, I obtanied some unexpected very interesting results concerning some hierachy structures about higher uniruledness structure. Here, higher uniruledness structure is, roughly speaking ,
represents how many independent lines are passing through each point of a given algebro-geometric object. Surfaces whose arbitrary point is contained in at least one line are called ruled surfaces, and are sometimes found in architecture also.
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| Academic Significance and Societal Importance of the Research Achievements |
考察の対象が複雑な場合，適当な同値関係を導入して考察の対象を簡単なものにすることは，日常生活でも良く行います．このような操作を抽象的に研究するのがホモトピー論ですが，より直観的な幾何的に展開しても納得できる意味で同値であることがGrothendieck,Kanらにより知られています．そして，Hopkins-Smithらにより，幾何的対象の客観的データを与えるコホモロジー論というものを用いて，更なる同一視を要請した安定ホモトピー論において，有る階層構造が得られました．本研究は，このような古典的ホモトピー論を含むA1(安定)ホモトピー論への大域的性質への応用と，代数幾何自身への応用が期待されます．
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