| Project/Area Number |
16340004
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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 Kyoto University, Research Institute for Mathematical Sciences, Professor (00093328)
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| Co-Investigator(Kenkyū-buntansha) |
MUKAI Shigeru Kyoto University, Research Institute for Mathematical Sciences, Professor (80115641)
NAKAYAMA Noboru Kyoto University, Research Institute for Mathematical Sciences, Associate Professor (10189079)
KAWAKITA Masayuki Kyoto University, Research Institute for Mathematical Sciences, Associate Professor (10378961)
NAMIKAWA Yoshinori Osaka University, Graduate School of Science, Professor (80228080)
OGISO Keiji Keio University, Faculty of Economies, Professor (40224133)
斎藤 盛彦 京都大学, 数理解析研究所, 准教授 (10186968)
高木 寛通 東京大学, 数理科学研究科, 助教授 (30322150)
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| Project Period (FY) |
2004 – 2007
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| Project Status |
Completed (Fiscal Year 2007)
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| Budget Amount *help |
¥9,200,000 (Direct Cost: ¥8,600,000、Indirect Cost: ¥600,000)
Fiscal Year 2007: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2006: ¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 2005: ¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 2004: ¥2,600,000 (Direct Cost: ¥2,600,000)
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| Keywords | Q-conic bundle / K3 surface / Terminal singularity / divisorial contraction / flop / complex symplectic variety / Fano variety / minimal model theory / 端射線 / del Pezzo曲面 / 逆同伴 / 乗数イデアル / ポアソン変形 / モジュライ空間 / シンプレクテイック特異点 / 変形 / 対数的標準特異点 / b関数 / フリップ / 標準特異点 / general elephant予想 / 因子収縮写像 / 導来圏 / Fano多様体 / Zariski分解 / Chow群 |
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| Research Abstract |
Mori, jointly with Prokhorov, proved Iskovskikh's conjecture on the singular points of the base surface of a 3-dimensional terminal Q-conic bundle, and classified the fibers over the points. Mukai explicitly described the K3 surfaces with primitive polarization of degree 24, and proved the unirationality of the moduli and universal family. Namikawa explicitly described the equivalence of the derived categories of coherent sheaves for Mukai flops. He also moved the equivalence of deformation smoothability and existence of a crepent resolution for projective complex symplectic varieties. Nakayama published the numerical study on divisors of algebraic varieties. Jointly with Fujimoto, he determined the structure of a nonsingular projective 3-fold with non-negaive Kodaira dimension and with a surjective self morphism of degree >1. Kawakita published the classification of 3-dimensional divisorial contractions contracting a divisor to a non-Gorenstein point. He proved the inverse adjunction
… More
for log canonicity. Oguiso, jointly with Hosono, Lian and Yau, gave an explicit formula for the number of the Fourier Mukai pairs for a complex projective K3 surface. He else determined the maximal finite solvable group acting on some complex K3 surface. Takagi classified the primary singular Fano threefolds with only quotient terminal singularities satisfying General Elephant Conjecture on anti-canonical systems. Saito, jointly with Budur and Mustata, gave a combinatorial formula on the b-function of a principal ideal, defined the b-function for an arbitrary ideal, and proved its relation with multiplier ideals. Abe studied how the moduli of vector bundles with fixed determinant bundle degenerates when the base curve degenerates to a nodal curve. Hayakawa revised and proved Reid's conjecture on the existence of an economical blowup of a 3-dimensional terminal singularity. The overseas cooperative researcher Matsuki successfully revised the invariant and bipassed the termination conjecture in his project with Kawanoue toward desingularization in positive characteristics. Less
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