| Project/Area Number |
14204001
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Nagoya University |
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Principal Investigator |
KONDO Shigeyuki Nagoya University, Graduate School of Mathematics, Professor, 大学院・多元数理科学研究科, 教授 (50186847)
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| Co-Investigator(Kenkyū-buntansha) |
UMEMURA Hiroshi Nagoya University, Graduate School of Mathematics, Professor, 大学院・多元数理科学研究科, 教授 (40022678)
TSUCHIYA Akihiro Nagoya University, Graduate School of Mathematics, Professor, 大学院・多元数理科学研究科, 教授 (90022673)
YOSHIKAWA Ken-ichi University of Tokyo, Graduate School of Mathematics, Associate Professor, 大学院・数理科学研究科, 助教授 (20242810)
FUJINO Osamu Nagoya University, Graduate School of Mathematics, Associate Professor, 大学院・多元数理科学研究科, 助教授 (60324711)
ITO Yukari Nagoya University, Graduate School of Mathematics, Associate Professor, 大学院・多元数理科学研究科, 講師 (70285089)
藤原 一宏 名古屋大学, 大学院・多元数理科学研究科, 教授 (00229064)
坂内 健一 名古屋大学, 大学院・多元数理科学研究科, 助手 (90343201)
宇沢 達 名古屋大学, 大学院・多元数理科学研究科, 教授 (40232813)
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| Project Period (FY) |
2002 – 2005
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| Project Status |
Completed (Fiscal Year 2005)
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| Budget Amount *help |
¥36,140,000 (Direct Cost: ¥27,800,000、Indirect Cost: ¥8,340,000)
Fiscal Year 2005: ¥8,190,000 (Direct Cost: ¥6,300,000、Indirect Cost: ¥1,890,000)
Fiscal Year 2004: ¥8,060,000 (Direct Cost: ¥6,200,000、Indirect Cost: ¥1,860,000)
Fiscal Year 2003: ¥8,320,000 (Direct Cost: ¥6,400,000、Indirect Cost: ¥1,920,000)
Fiscal Year 2002: ¥11,570,000 (Direct Cost: ¥8,900,000、Indirect Cost: ¥2,670,000)
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| Keywords | Moduli / Automorphic form / Del Pezzo surface / K3 surface / モジュライ空間 / 三次曲面 / 一意化 / 3次曲面 / 複素ボール / 自己同型群 / Leech格子 |
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| Research Abstract |
In this project we gave a description of the moduli space of del Pezzo surfaces as an arithmetic quotient of a complex ball by means of the theory of periods of K3 surfaces. By the same method, we showed that the moduli space of 8 points on the projective line can be written as an arithmetic quotient of 5-dimensional complex ball. Moreover we gave a relation of our description and the theory of complex reflection groups due to Deligne-Mostow. On the other hand, by using the theory of automorphic forms on a bounded symmetric domain of type IV, we gave a projective model of the moduli of 8 points on the projective line which coincides with the classical one defined by the cross ratio.
It is not well known that K3 surfaces in positive characteristic. In this project, we studied the most special supersingular K3 surface in characteristic 2. Also we gave a few new examples of supersingular K3 surfaces on which Mathieu groups of degree 11 and 22 act symplectic automorphisms.
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