| Project/Area Number |
22224001
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| Research Category |
Grant-in-Aid for Scientific Research (S)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Nagoya University |
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Principal Investigator |
KONDO Shigeyuki 名古屋大学, 多元数理科学研究科, 教授 (50186847)
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| Co-Investigator(Kenkyū-buntansha) |
EGUCHI Toru 立教大学, 理学研究科, 教授 (20151970)
ITO Yukari 名古屋大学, 大学院多元数理科学研究科, 准教授 (70285089)
IYAMA Osamu 名古屋大学, 大学院多元数理科学研究科, 教授 (70347532)
MA Shohei 東京工業大学, 理学研究科, 准教授 (80633255)
KANNO Hiroaki 名古屋大学, 大学院多元数理科学研究科, 教授 (90211870)
NAGAO Kentaro (元)名古屋大学, 大学院多元数理科学研究科, 助教 (10585574)
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| Co-Investigator(Renkei-kenkyūsha) |
MUKAI Shigeru 京都大学, 数理解析研究所, 教授 (80115641)
SHIMADA Ichiro 広島大学, 理学研究科, 教授 (10235616)
OGISO Keiji 大阪大学, 理学研究科, 教授 (40224133)
YOSHIKAWA Kenichi 京都大学, 理学研究科, 教授 (20242810)
MIYAMOTO Masahiko 筑波大学, 理学研究科, 教授 (30125356)
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| Project Period (FY) |
2010-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥76,180,000 (Direct Cost: ¥58,600,000、Indirect Cost: ¥17,580,000)
Fiscal Year 2014: ¥15,730,000 (Direct Cost: ¥12,100,000、Indirect Cost: ¥3,630,000)
Fiscal Year 2013: ¥15,470,000 (Direct Cost: ¥11,900,000、Indirect Cost: ¥3,570,000)
Fiscal Year 2012: ¥16,120,000 (Direct Cost: ¥12,400,000、Indirect Cost: ¥3,720,000)
Fiscal Year 2011: ¥15,080,000 (Direct Cost: ¥11,600,000、Indirect Cost: ¥3,480,000)
Fiscal Year 2010: ¥13,780,000 (Direct Cost: ¥10,600,000、Indirect Cost: ¥3,180,000)
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| Keywords | 格子 / 保型形式 / モジュライ / K3 曲面 / エンリケス曲面 / マシュームーンシャイン / 自己同型 / マシュー群 / マシュー・ムーンシャイン / 数学 / 代数幾何学 / K３曲面 / 格子理論 / 代数学 / モジュライ空間 / 代数 / 代数幾何 / K3曲面 / Calabi-Yau多様体 |
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| Outline of Final Research Achievements |
The main problem of algebraic geometry is to study structures and symmetries of algebraic varieties and their moduli spaces. A K3 surface is a 2-dimensional analogue of an elliptic curve, which was found in the 19th century. Now K3 surfaces are interesting to Mathematics and theoretical Physics. In this research project we have obtained several results of the structure of moduli spaces of K3 surfaces and automorphisms of K3 surfaces. On the other hand, there is a mysterious connection, called Mathieu moonshine, between symmetries of K3 surfaces and the Mathieu group, a sporadic finite simple group. We have some results concerning this phenomenon.
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| Assessment Rating |
Verification Result (Rating)
A
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Assessment Rating |
Result (Rating)
A: Progress in the research is steadily towards the initial goal. Expected research results are expected.
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