2002 Fiscal Year Final Research Report Summary
A study on dynamical system for a torus and cohomology
| Project/Area Number |
12640183
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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 | KYUSHU UNIVERSITY |
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Principal Investigator |
KAZAMA Hideaki Faculty of Math. Prof., 数理学研究院, 教授 (10037252)
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| Co-Investigator(Kenkyū-buntansha) |
CHOU Kanji Faculty of Math. Associate Prof., 数理学研究院, 助教授 (10197634)
FURUSHIMA Mikio Kumamoto Univ. Faculty of Science, Prof., 理学部, 教授 (00165482)
KANEKO Shouichi Ryukyu Univ. Faculty of Science, Prof., 理学部, 教授 (10194911)
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| Project Period (FY) |
2000 – 2002
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| Keywords | line bundle / Kodaira's lemma / toroidal group |
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| Research Abstract |
(I) It is a problem whether one can embed a weakly 1-complete manifold with a positive line bundles into a projective space by sections of higher tensor power positive line bundles, or not. It is a very interesting result that one can embed a weakly 1-complete manifold with a positive line bundle by sections of adjoint line bundles instead of the original line bundle by Shigeharu Takayama. This result is proved by a similar method in case of compact manifolds. We apply this method by adjoint line bundle to a problem of line bundle convexity. We get some global result with respect to line bundle convexity of weakly 1-complete manifolds.
(ii) Recently we find an example that Kodaira's lemma does not hold for some strongly 1-complete manifold. Now we try to characterize strongly 1-complete manifolds on which Kodaira's lemma holds alway.
(iii) On troidal groups of cohomologically finite type we can apply the theory of compact Kaehler manifolds. For instance we can show the Hodge decomposition theorem for toroidal groups of cohomologically finite type. We are getting some result for them similar to the results of compact Kaehler manifolds.
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