| Project/Area Number |
14340041
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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 |
Basic analysis
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| Research Institution | Nagoya University |
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Principal Investigator |
OHSAWA Takeo Nagoya University, Mathematics, Professor, 大学院・多元数理科学研究科, 教授 (30115802)
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| Co-Investigator(Kenkyū-buntansha) |
MIYAKE Masatake Nagoya University, Mathematics, Professor, 大学院・多元数理科学研究科, 教授 (70019496)
SUZUKI Nariaki Nagoya University, Mathematics, Associate Professor, 大学院・多元数理科学研究科, 助教授 (50154563)
吉川 謙一 東京大学, 大学院・数理科学研究科, 助教授 (20242810)
平地 健吾 東京大学, 大学院・数理科学研究科, 助教授 (60218790)
中西 敏浩 名古屋大学, 大学院・多元数理科学研究科, 助教授 (00172354)
神本 丈 九州大学, 大学院・数理学研究科, 助教授 (90301374)
高山 茂晴 九州大学, 大学院・数理学研究科, 助教授 (20284333)
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| Project Period (FY) |
2002 – 2005
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| Project Status |
Completed (Fiscal Year 2005)
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| Budget Amount *help |
¥13,600,000 (Direct Cost: ¥13,600,000)
Fiscal Year 2005: ¥4,900,000 (Direct Cost: ¥4,900,000)
Fiscal Year 2004: ¥2,800,000 (Direct Cost: ¥2,800,000)
Fiscal Year 2003: ¥2,800,000 (Direct Cost: ¥2,800,000)
Fiscal Year 2002: ¥3,100,000 (Direct Cost: ¥3,100,000)
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| Keywords | complex manifolds / holomorphic vector bundle / extension theorem / Levi flat / Kahler manifolds / Stein manifolds / コモホロジー入射性定理 / ∞でのベルグマン核の挙動 / レヴィ平坦超曲面 / 2次元複素トーラス / L^2正則関数 / Bergman計量 / 変形剛性 / Bergman空間 / 強擬凸領域 / Hardy空間 / コホモロジー入射性定理 / モデル領域 / 漸近解析 / Bergman核 / 擬凸領域 |
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| Research Abstract |
Let M be a complex manifold, let S be a complex analytic subset of M and let E →M be a holomorphic vector bundle. Concerning the extension problem for holomorphic sections of E from S to M, we obtained the following.
Theorem, Let M be a weakly 1-complete Kahler manifold, let (E, h) be a Hermitian holomorphic vector bundle over M, and let (L, b) be a Hermitian holomorphic line bundle over M. For the curvature forms 【encircled H】_h and 【encircled H】_b of h and b, assume that 【encircled H】_h 【greater than or equal】 0 and 【encircled H】_h-εId_E【cross product】【encircled H】_b hold for some ε>0. Then, for any nonzero holomorphic section S of L, the homomorphism s : H^q(M, K_M【cross product】E) →H^q(M, K_M【cross product】E【cross product】L) has a kernel contained in the closure of zero.
We obtained also several results on Levi flat hypersurfaces.
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