2005 Fiscal Year Final Research Report Summary
Global complex analysis - around L^2 holomorphic functions
| 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)
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| Project Period (FY) |
2002 – 2005
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| Keywords | complex manifolds / holomorphic vector bundle / extension theorem / Levi flat / Kahler manifolds / Stein manifolds |
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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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