1996 Fiscal Year Final Research Report Summary
Uniformization Theorems on Manifolds
| Project/Area Number |
08454015
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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 |
Geometry
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
FUTAKI Akito Tokyo Institute of Technology, Faculty of Science, Professor, 理学部, 教授 (90143247)
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| Co-Investigator(Kenkyū-buntansha) |
HATTORI Toshiaki Tokyo Institute of Technology, Faculty of Science, Research Associate, 理学部, 助手 (30251599)
TSUJI Hajime Tokyo Institute of Technology, Faculty of Science, Assistant Professor, 理学部, 助教授 (30172000)
ISHII Shihoko Tokyo Institute of Technology, Faculty of Science, Assistant Professor, 理学部, 助教授 (60202933)
KUROKAWA Nobushige Tokyo Institute of Technology, Faculty of Science, Professor, 理学部, 教授 (70114866)
TANNO Shukiti Tokyo Institute of Technology, Faculty of Science, Professor, 理学部, 教授 (10004293)
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| Project Period (FY) |
1996
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| Keywords | Einstein metrics / Futaki Character / Minimal hypersurface / Singularity / Algebraic variety |
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| Research Abstract |
Futaki studied on the relationship between the existence of Kaehler-Einstein metrics, stability of algebraic manifolds in the sense of Mumford and the nontriviality of the Futaki character.
Tanno studied on the conjecture that there would not exist any L^2 harmonic forms on complete stable minimal hypersurfaces in Euclideam (m+1)-space, and proved affirmatively for m<5.
Ishii constructed canonical models, minimal models and logarythmic canonical models for arbitrary nondegenerate hypersurface singularities. She also constructed minimal models for divisors of toric varieties. She construted a counter-example to a conjecture of Reid concerning canonical singularities. Tsuji analyzed the structure of canonical rings using singular metrics. He considered a construction of the moduli spaces of algebraic varieties of general type.
Hattori considered the case where the holonomy groups induced by the projevtive structures on Riemann sufaces are discrete, and showed that only pseudo Fuchsian groups can appear when they are stable.
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