| Project/Area Number |
12440005
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | KYOTO UNIVERSITY |
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Principal Investigator |
MORI Shigefumi MORI,Shigefumi, 数理解析研究所, 教授 (00093328)
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| Co-Investigator(Kenkyū-buntansha) |
NAMIKAWA Yoshinori KYOTO UNIVERSITY, Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (80228080)
NAKAYAMA Noboru Research Institute for Mathematical Sciences, Associate Professor, 数理解析研究所, 助教授 (10189079)
MUKAI Shigeru Research Institute for Mathematical Sciences, Professor, 数理解析研究所, 教授 (80115641)
OGUISO Keiji The University of Tokyo, Graduate School of Mathematical Science, Associate Professor, 大学院・数理科学研究科, 助教授 (40224133)
SAITO Masa-hiko Kobe University, Faculty of Science, Professor, 理学部, 教授 (80183044)
宮岡 洋一 東京大学, 大学院・数理科学研究科, 教授 (50101077)
藤野 修 京都大学, 数理解析研究所, 助手 (60324711)
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| Project Period (FY) |
2000 – 2003
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| Project Status |
Completed (Fiscal Year 2003)
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| Budget Amount *help |
¥6,500,000 (Direct Cost: ¥6,500,000)
Fiscal Year 2003: ¥1,600,000 (Direct Cost: ¥1,600,000)
Fiscal Year 2002: ¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 2001: ¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 2000: ¥1,900,000 (Direct Cost: ¥1,900,000)
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| Keywords | flip / flop / Fano 3-fold / canonical divisor / symplectic variety / extremal neighborhood / elliptic structure / terminal singularity / symplectic singularity / invariants / monodromy / derived category / K3 surface / complex symplectic structure / Painleve equation / Calabi-Yau threefold / deformation theory / cononical bundle / Calabi-Yau 3-fold / Gorenstein singularity / eliptic surface / 端末特異点 / 端射線 / Fano多様体 / シンプレクティック多様体 / フリップ / Painleve微分方程式 / ケーラー錐 / K3曲面 |
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| Research Abstract |
Mori and Fujino have generalized Kodaira's canonical bundle formula and proved, as an application, that algebraic varieties with Kodaira dimension at most three have finitely generated canonical rings. Mori, Miyaoka and Takagi, together with Kollar, have proved the boundedness of Fano 3-folds with only canonical singularities. Mori also gave an explicit description of every irreducible semistable extremal neighborhood with two non-Gorenstein points, in terms of coordinates with equations and patching.
Mukai proved that every canonical curve of genus 9 with maximal Clifford index, is a linear space section of the symplectic Grassmannian variety of dimension six.
Masahiko Saito have introduced the Okamoto-Painleve pair of an algebraic surface and its anti-canonical divisor which algebro-geometrically characterizes the initial value space of the Painleve equation. He also reconstructed the Painleve equation from the pair using its deformation theory.
Nakayama described certain elliptic fiber structures over a given analytic space upto bimeromorphic equivalence using the a-etale cohomology group.
Namikawa have studied birational maps between complex symplectic varieties and proved that the analogue of "Reid's dream" does not hold in the category of complex symplectic varieties. He also constructed a counterexample to birational Torelli problem for complex symplectic varieties.
Oguiso has generalized the characterization of the Klein curve to the case of K3 surfaces, which states that the Klein-Mukai surface is the only K3 surface which admits a faithful action of the quartic extension of the simple group of order 168.
Takagi has generalized Takeuchi's method, obtained a classification list of Q-Fano 3-folds with index two and confirmed the existence in several cases.
Fujino has proved that every sequence of log flips terminates for 4 dimensional canonical pairs.
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