| Project/Area Number |
25800018
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Kobe University |
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Principal Investigator |
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| Research Collaborator |
NAKAMURA Iku 北海道大学, 大学院理学研究科, 名誉教授 (50022687)
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 代数曲線束 / 楕円曲面 / 正標数 / 分離商 / 純非分離商 / 曲線束 / 退化ファイバー / 主等質空間 / 整モデル / ガロワ・コホモロジー / 非分離商 / 曲面 / 商特異点 / 特異点解消 / トーリック幾何 / 分離商と純非分離商 / 特異ファイバー / リジッド幾何 / 正標数代数幾何 / 代数曲面 / アーベル多様体 / p進一意化 |
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| Outline of Final Research Achievements |
In algebraic geometry, the classification of algebraic varieties is one of the most fundamental problems, where algebraic varieties are classified by means of their geometric invariants. We consider the case where algebraic varieties are surfaces that are fibered over curves. We develop the methods to calculate invariants of algebraic varieties, which are important in the classification theory. Algebraic varieties are defined as the solutions of simultaneous polynomial equations. In our studies, these polynomials are defined over not only the field of complex numbers but also more general fields. In particular, in the case of fields of positive characteristic, various new phenomena appear, and we develop theories to explain them.
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