| Project/Area Number |
04302003
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| Research Category |
Grant-in-Aid for Co-operative Research (A)
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| Allocation Type | Single-year Grants |
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| Research Field |
代数学・幾何学
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| Research Institution | KYOTO UNIVERSITY |
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Principal Investigator |
MARUYAMA Masaki Kyoto Univ. Fac.of Sci.Professor, 理学部, 教授 (50025459)
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| Co-Investigator(Kenkyū-buntansha) |
KAWAMATA Yujiro Univ.of Tokyo Dept.of Math.Sci.Professor, 大学院・数理科学研究科, 教授 (90126037)
SUWA Tashuo Hokkaido Univ.Fac.of Sci.Professor, 理学部, 教授 (40109418)
IITAKA Shigeru Gakushuin Univ.Fac.of Sci.Professor, 理学部, 教授 (20011588)
ODA Tadao Tohoku Univ.Fac.of Sci.Professor, 理学部, 教授 (60022555)
UENO Kenji Kyoto Univ.Fac.of Sci.Professor, 理学部, 教授 (40011655)
宮西 正宜 大阪大学, 理学部, 教授 (80025311)
向井 茂 名古屋大学, 理学部, 教授 (80115641)
森 重文 京都大学, 数理解析研究所, 教授 (00093328)
渡辺 敬一 東海大学, 情報数理, 教授 (10087083)
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| Project Period (FY) |
1992 – 1994
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| Project Status |
Completed (Fiscal Year 1994)
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| Budget Amount *help |
¥19,300,000 (Direct Cost: ¥19,300,000)
Fiscal Year 1994: ¥4,200,000 (Direct Cost: ¥4,200,000)
Fiscal Year 1993: ¥7,800,000 (Direct Cost: ¥7,800,000)
Fiscal Year 1992: ¥7,300,000 (Direct Cost: ¥7,300,000)
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| Keywords | Algebraic Geometry / Algebraic Variety / Classification of Algebraic Varieties / Kahler Manifold / Conformal Field Theory / Stable Sheaves / Vector Bundle / Moduli / 代数多様体の変形 / モデュライ理論 / ホッジ理論 / 可換環論 / 算術的代数幾何学 / 代数様体 / モジュライ / 算術的代数多様体 / Hodge-理論 / 放物束 / 特異点 |
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| Research Abstract |
In the last few decades the study on algebraic varieties has been very active. Not only algebraic varieties itself but also the fertility of the structures over algebraic varieties are attracting the scholars of algebra and geometry. Moreover, as we can see in the research of the conformal field theory and the Calabi-Yau manifolds, the relationship with various fields including physics is getting closer. In this project, paying attention to the interrelation among actions of groups on algebraic varieties, Hodge theory and period maps of Kahler manifolds, various moduli spaces on algebraic varieties, conformal field theory on arithmetic varieties, K-theory and number theory, we tried to make great progress in studying algebraic variety, In addition to individual studies in the neighborhoods of investigators, we organized several conferences to design close communication between related fields and sent members of the project to relevant conferences.
We could get the following excellent results : construction of the moduli space of parabolic stable sheaves, study and applications of its structure, construction of the moduli space of stable sheaves on prejective schemes that may be singular, conformal field theory from the mathematical viewpoint, constructions, deformations and mirror symmetries of Calabi-Yau manifolds, development and applications of Model-Weil lattices, study and applications of K3 surfaces, existence prpblem of the surfaces of general type, development of Mori theory.
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