2007 Fiscal Year Final Research Report Summary
Uniqueness problem and deficient divisors of meromorphic mappings
| Project/Area Number |
17540184
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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 | Numazu College of Technology |
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Principal Investigator |
AIHARA Yoshihiro Numazu College of Technology, Division of Liberal Arts, Professor (60175718)
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| Co-Investigator(Kenkyū-buntansha) |
MORI Seiki Yamagata University, Department of Science, Professor (80004456)
KITAGAWA Yoshihisa Utsunomiya University, Department of Education, Professor (20144917)
ATSUJI Atsushi Keio University, Department of Economics, Professor (00221044)
KAMADA Hiroyuki Miyagi University of Education, Department of Education, Associate Professor (00249799)
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| Project Period (FY) |
2005 – 2007
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| Keywords | meromorpphic mapping / uniqueness problem / Nevanlinna theory / deficiency / Khaeler manifold / flat torus / indefinite Khaeler metric / scalar curvature |
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| Research Abstract |
The investigator Aihara studied uniqueness theorems for finite sheeted analytic covering spaces over the complex m-space. Some finiteness theorem and unicity theorems are obtained. Aihara also studied deficiencies of holomorphic curves as functions on linear systems over a projective algebraic manifold M. He define the deficiency for the base locus of linear systems by means of the new language in the value distribution theory for coherent ideal sheaves. In particular, he prove that there exists the correspondence between the deficiency and the linear system with the non-empty base locus.
The investigator Mori studied unique range set for meromorphic functions of one complex variable and proved some unicity theorems. In particular, he give an improvement of Nevanlinna's four points theorem. The investigator Kitagawa studied the rigidity of flat tori in the unit 3-sphere. His study is concerning on the conjecture that the diameter of all flat tori in the unit 3-sphere eqials π and he gave some conditions that are equivalent to this conjecture.
The investigator Atsuji studied Nevanlinna theory on complete Khaeler manifolds. His method is based on the heat kernel. He also studied meromorphic functions on a submanifold in the complex m-space and obtained precise estimate for defect relation.
The investigator Kamada studied hyper-CR structure and quarternion CR structure. He studied pseudoconvexity of such structures. He also studied conditions under which complex manifolds admit such structures.
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Research Products
(40 results)
