1999 Fiscal Year Final Research Report Summary
Projective structures on compex manifolds
| Project/Area Number |
09640129
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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, Department of Mathematics, Professor, 理工学部, 教授 (90062679)
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| Co-Investigator(Kenkyū-buntansha) |
TAHARA Hidetoshi Sophia University, Department of Mathematics, Professor, 理工学部, 教授 (60101028)
KANEYUKI Soji Sophia University, Department of Mathematics, Professor, 理工学部, 教授 (40022553)
NAGANO Tadashi Sophia University, Department of Mathematics, Professor, 理工学部, 教授 (10189144)
YOKOYAMA Kazuo Sophia University, Department of Mathematics, Asso. Professor, 理工学部, 助教授 (10053711)
MIYAOKA Reiko Sophia University, Department of Mathematics, Professor, 理工学部, 教授 (70108182)
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| Project Period (FY) |
1997 – 1999
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| Keywords | complex manifold / projective structure / Gauduchon metric / Hartogs domain / non-Kahler / extension peoblem |
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| Research Abstract |
Our main object of study is a class of compact complex 3-manifolds which contain a subdomain U biholomorphic to a neighborhood of a projective line ill a complex projective 3-space. We call such a class of manifolds by Class L. Such manifolds do not admit projective structures in general, but very deeply related to complex manifolds which admit projective structures. To classify all Class L. manifolds, it seems very important to consider the existence problem of Cauduchon metric near a singular fibre of a 1-parameter family of surfaces, and we are now very near to the complete solution.
To carry out our plan of classification of Class L manifolds, a series of theorems of S. Ivashkovich on the extension of meromorphic maps play important roles. On the other hand, our manifolds of Class L supply us with many interesting examples on extension problems of meromorphic maps. N. Okada (Sophia Univ. Graduate Course) constructed an example of Schottky type Class L manifolds, gave a holomorphic map of a Hartogs domain to the manifold whichl cannot he extended meromorphically across a fractal set, and estimated the Hausdorff dimension of the singular set. With Y. Kamozawa (NTT), we have obtained a explicit formula of characteristic forms on a holomorphic foliation which admits a holomorphic projective connection.
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