Projective Algebraic Geometry in Positive Characteristic
| Project/Area Number |
16K05113
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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 |
Algebra
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| Research Institution | Waseda University |
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Principal Investigator |
KAJI Hajime 早稲田大学, 理工学術院, 教授 (70194727)
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| Project Period (FY) |
2016-04-01 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2019: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | 射影多様体 / 正標数 / ガウス写像 / 双対多様体 / 接的退化曲線 / グラスマン束 / 次数公式 / 射影双対 / 再帰性 / 代数幾何 |
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| Outline of Final Research Achievements |
In 1845, George Boole discovered a formula for the degree of dual manifolds of Veronese varieties. In general, the dual variety of a projective variety X is a closed variety of dual projective space given by the closure of the set of hyperplanes tangent to X. In the previous research, for Veronese varieties, we obtained an degree formula (unpublished) that generalizes dual varieties into images of general Gauss maps. In this research, we investigated the asymptotic behavior of the image degree of the general Gauss map of the Veronese varieties using the generalized degree formula.
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| Academic Significance and Societal Importance of the Research Achievements |
170年以上前にGeorge Booleにより発見されていたヴェロネーゼ多様体の双対多様体の次数公式に焦点を当てて研究をした.一般ガウス写像の像の次数に一般化した公式自体は,与えられた数の分割に対応する既約表現の次元を含む一見複雑なものとなったが,漸近的挙動について,上限・下限は意外に単純な式により, ある程度良く評価されることがわかった.
Booleの公式の一般化として他の多様体の双対多様体の次数公式は研究されてきたが,一般ガウス写像の像の次数については本研究で初めて扱われたものである.
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Report
(5 results)
Research Products
(12 results)
