2009 Fiscal Year Final Research Report
Extension property of holomorphic maps and the structure of complex manifolds
| Project/Area Number |
19540100
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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 University, 理工学部, 教授 (90062679)
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| Co-Investigator(Kenkyū-buntansha) |
YOKOYAMA Kazuo 上智大学, 理工学部, 准教授 (10053711)
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| Project Period (FY) |
2007 – 2009
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| Keywords | 幾何学 / 複素多様体 / 正則写像の拡張 / non-Kaehler, Klein群 |
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| Research Abstract |
We are studying a method to get some information of the structure of a given complex manifold by measuring the extendibility of holomorphic maps of Hartogs domains to the given manifold. As an application of the method, we have obtained the following result. For a finitely generated three dimensional discrete projective transformation group Γ with some discontinuity condition, we can define canonically a non-singular quotient space X(Γ) of an open subset of a projective 3-space. We have shown that, if X(Γ) contains a compact connected component with positive algebraic dimension, then X(Γ) is connected, and that X(Γ) is biholomorphic to one of the three kinds of well-known 3-folds.
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