| Project/Area Number |
16K13749
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Hiroshima University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
木村 俊一 広島大学, 理学研究科, 教授 (10284150)
奥田 隆幸 広島大学, 理学研究科, 講師 (40725131)
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| Project Period (FY) |
2016-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 格子 / 符号 / 計算機アルゴリズム / K3曲面 / コンフィギュレーション / Leech 格子 / Conway 群 / extremal 格子 / 代数幾何学 / 組合せ論的構造 / フェルマー多様体 |
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| Outline of Final Research Achievements |
We investigated various algebraic varieties from combinatorial point of view, and observed many interesting facts. During the investigation, we improved several algorithms for combinatorial calculations, and implemented them in our computers. Thanks to these algorithms, we have succeeded in probing geometric properties of some K3 and Enriques surfaces, and in particular, determined their automorphism groups.
We also made huge data about the Leech lattice. We hope this data will be helpful in future investigation of algebraic varieties from combinatorial point of view.
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| Academic Significance and Societal Importance of the Research Achievements |
格子や符号といった組み合わせ論的な数学的対象は，安全で高速なデジタル通信を支える上で重要な役割を果たしており，良い格子，良い符号，良い組み合わせ論的対象を見つけることは数学の重要な課題の一つである．特に，対称性の高い特別な代数多様体の幾何学からは興味深い組み合わせ論的構造が得られることが多い．本研究においては，様々な代数多様体に現れる興味深い組み合わせ論的構造を調べた．
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