| Project/Area Number |
07404001
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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 | Tohoku University |
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Principal Investigator |
ODA Tadao Graduate School of Science, Tohoku University, Professor, 大学院・理学研究科, 教授 (60022555)
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| Co-Investigator(Kenkyū-buntansha) |
TAKAGI Izumi Graduate School of Science, Tohoku University, Professor, 大学院・理学研究科, 教授 (40154744)
ISHIDA Masanori Graduate School of Science, Tohoku University, Professor, 大学院・理学研究科, 教授 (30124548)
NISHIKAWA Seiki Graduate School of Science, Tohoku University, Professor, 大学院・理学研究科, 教授 (60004488)
SUNADA Toshikazu Graduate School of Science, Tohoku University, Professor, 大学院・理学研究科, 教授 (20022741)
MORITA Yasuo Graduate School of Science, Tohoku University, Professor, 大学院・理学研究科, 教授 (20011653)
板東 重稔 (坂東 重稔) 東北大学, 大学院・理学研究科, 教授 (40165064)
新井 仁之 東北大学, 大学院・理学研究科, 教授 (10175953)
堀田 良之 東北大学, 大学院・理学研究科, 教授 (70028190)
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| Project Period (FY) |
1995 – 1998
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| Project Status |
Completed (Fiscal Year 1998)
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| Budget Amount *help |
¥13,900,000 (Direct Cost: ¥13,900,000)
Fiscal Year 1998: ¥3,300,000 (Direct Cost: ¥3,300,000)
Fiscal Year 1997: ¥2,600,000 (Direct Cost: ¥2,600,000)
Fiscal Year 1996: ¥3,000,000 (Direct Cost: ¥3,000,000)
Fiscal Year 1995: ¥5,000,000 (Direct Cost: ¥5,000,000)
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| Keywords | toric variety / intersection cohomology / fundamental group / Laplacian / discrete spectrum / reaction-diffusion equation / Kaehler manifold / conformally flat manifold / スペクトル幾何 / 拡散反応方程式 / アインシュタイ・エルミート計量 / 有理点 / シュレーディンガー作用素 / ミンコフスキー和 / アーベル多様体 / リーマン多様体 / 複素数多様体 / 微分作用素 / 非線型微分方程式 / トーリック幾何 / アーベル曲面 / スペクトル / 調和写像 / 反応拡散方程式系 / アインシュタイン計量 / 非アルキメデス的多様体 / 代数的対称空間 / D加群 / テイト予想 / エルゴード性 / p進多様体 / ベクトル束 |
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| Research Abstract |
Through close contact and discussion among the investigators, comprehensive study was made on various problems on manifolds.
1. Toric varieties were studied from the aspects of algebraic geometry, algebraic analysis and differential geometry, and new results were obtained on intersection cohomology, morphisms to toric varieties, classification of toric Fano manifolds and Einstein-Kaehler metrics.
2. Arithmetic varieties were studies, and new results were obtained on rational points on Abelian surfaces, the Tate conjecture on the second etale cohomology, crystal fundamental group and rho-adic Hodge theory.
3. Rigidity results were obtained for non-Archimedean varieties.
4. Various new results were obtained on the global analysis, hyperbolic geometry and fundamental groups of differentiable manifolds, Riemannian manifolds, and conformally flat manifolds.
5. Laplacian and Schroedinger operators were studies from the viewpoint of analysis and mathematical physics, and new interesting results were obtained on the discrete analog on graphs.
6. Global study was made on reaction-diffusion equations, and new results were obtained on the stability of solutions.
7. Various new results were obtained on the stability of vector bundles on Kaehler manifolds and Einstein-Hermitian metics.
8. Pseudo-differential operators, maximal operators, bounded linear operators, operator algebras were studies from the viewpoint of real analysis, complex analysis and Fourier analysis.
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