| Project/Area Number |
24540053
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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 | Hosei University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
KONDO Shigeyuki 名古屋大学, 大学院多元数理科学研究科, 教授 (50186847)
SHIMADA Ichiro 広島大学, 大学院理学研究科, 教授 (10235616)
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| Research Collaborator |
GEER Gerard Van Der Universiteit van Amsterdam, Korteweg-de Vries Instituut, Professor
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2013: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2012: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
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| Keywords | カラビ・ヤウ多様体 / K3曲面 / アーベル曲面 / 正標数 / 有理曲線 / 楕円曲線 / ネロン・セヴェリ群 / 直線配置 / 超特異 / 超特殊 / 国際研究者交流（オランダ） / クンマー曲面 / リーチ格子 / ピカール格子 |
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| Outline of Final Research Achievements |
Calabi-Yau varieties are very important varieties both in mathematics and in physics (theory of elementary particles). In this research, I examined the structure of Calabi-Yau varieties, in particular, K3 surfaces (two-dimensional Calabi-Yau varieties) in characteristic p >0. In fact, on the superspecial K3 surface in characteristic 5, there exist 96 smooth rational curves, and they are divided into 6 groups. Any two curves in the same group don't intersect each other, and if we choose two groups among six, the curves in the two groups make a beautiful configuration. I had also obtain several results on the structure of Chern class maps of abelian surfaces, geometric invariants of algebraic varieties in positive characteristic, and the structure of lines on a certain Fermat hypersurface in the 3-dimensional projective space. I announced in total 4 papers on these results.
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