| Project/Area Number |
62460002
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| Research Category |
Grant-in-Aid for General Scientific Research (B)
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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 | TOHOKU UNIVERSITY |
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Principal Investigator |
ODA Tadao Professor Faculty of Science,Tohoku University, 理学部, 教授 (60022555)
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| Co-Investigator(Kenkyū-buntansha) |
BANDO Shigetoshi Assista Faculty of Science,Tohoku University, 理学部, 助教授 (40165064)
ISHIDA Masa-Nori Assista Faculty of Science,Tohoku University, 理学部, 助教授 (30124548)
森田 康夫 東北大学, 理学部, 教授 (20011653)
HOTTA Ryoshi Professor Faculty of Science,Tohoku University, 理学部, 教授 (70028190)
SATAKE Ichiro Professor Faculty of Science,Tohoku University, 理学部, 教授 (00133934)
MORITA Yasuo Professor Faculty of Science,Tohoku University
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| Project Period (FY) |
1987 – 1988
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| Project Status |
Completed (Fiscal Year 1988)
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| Budget Amount *help |
¥4,600,000 (Direct Cost: ¥4,600,000)
Fiscal Year 1988: ¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 1987: ¥2,600,000 (Direct Cost: ¥2,600,000)
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| Keywords | Algebraic singularity / Complex analytic singularity / Toric variety / Zeta function / Affine Lie algebra / Conformal field theory / アインシュタイン・ケーラー計量 / ゼータ函数 / L函数 / ケーラー計量 / アヤィン・リー環 / トーリック因子 / 非ケーラー多様体 / 共形的場の理論 / アフィンワイル群 / ヘッケ環 |
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| Research Abstract |
1. We carried out investigations of algebraic and complex analytic singularities: (1) Analysis of infinitely very near singular points in arbitrary characteristics. (2) General theoretical formulation of the notion of toric divisors. (3) Construction of many new non-Kaehler manifolds.
2. In connection with automorphic functions, we studied zeta functions, L-functions from the point of view of their functional equations, residues and special values. We could find various important connections with the geometric properties of manifolds.
3. We carried out the following research on algebraic varieties and complex manifolds: (1) Birational geometry of toric varieties. (2) Unequal characteristic non-singular lifting of varieties with normal crossings. (3) Ricci-flat Kaehler metrics on affine algebraic manifolds. (4) Torelli problem for complete intersection varieties. (5) Construction and numerical invariants of regular algebraic surfaces of general type.
4. We carried out Lie-group-theoretic study of bounded domains as well as algebro-analytic study of Lie groups, algebraic groups, affine Lie algebras and their representations.
5. We could formulate two-dimensional conformal field theory in the framework of arithmetic algebraic geometry.
6. We exchanged research information with mathematicians inside and outside japan.
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