2006 Fiscal Year Final Research Report Summary
Extension property of holomorphic maps and complex structures of the target manifolds
| Project/Area Number |
17540094
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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 |
Geometry
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| Research Institution | Sophia University |
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Principal Investigator |
KATO Masahide Sophia Univ., Faculty of Science and Tech., Professor, 理工学部, 教授 (90062679)
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| Co-Investigator(Kenkyū-buntansha) |
TSUJI Hajime Sophia Univ., Faculty of Science and Tech., Professor, 理工学部, 教授 (30172000)
TAHARA Hidetoshi Sophia Univ., Faculty of Science and Tech., Professor, 理工学部, 教授 (60101028)
YOKOYAMA Kazuo Sophia Univ., Faculty of Science and Tech., Associate Professor, 理工学部, 助教授 (10053711)
AOYAGI Miki Tokyo Institute of Technology, Precision and intelligence Lab., Researcher, 精密工学研究所, 研究員 (90338434)
YAMADA Mikiko Sophia Univ., Faculty of Science and Tech., Assistant, 理工学部, 助手 (70384170)
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| Project Period (FY) |
2005 – 2006
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| Keywords | Extension of holomorphic map / Klein group / Complex projective structure / non-Kaehler |
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| Research Abstract |
1.We defined in our previous work an index which measures the extendibility of holomorphic maps of a Hartogs domain to complex manifolds. This index is useful to study quotient manifolds of "large" domains in complex projective 3-spaces. Here a domain in projective 3-space P^3 is "large", if the domain contains projective lines. Main result in this direction is the characterization of compact quotient of large domains with positive algebraic dimension. In this case, the large domain is dense in P^3 and the compement is very thin. Under an additional assumption, we could show that the quotient manifold is a P^3, a Blanchard manifold, or a L-Hopf manifold. We think that this additional assumption can be removed soon. To obtain this result we use also a recent result of S.Ivashkovich on extension of holomorphic maps into non-Kaehler manifolds.
2.The result above is an analogy of the elementary type group case in Klein group theory of complex 1-dimension and suggests a possibility of constructing higher dimensional complex analytic Klein group theory. We could give basic definitions to develop 3-dimensional complex analytic Klein group theory and formulate many problems.
3.Our research plan in the early stage was to seek good sufficient conditions of complex manifolds to be "probable". At present we have no results in this direction.
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