1999 Fiscal Year Final Research Report Summary
On the value distribution of meromorphic mappings (the uniqueness problem and the existence problem of deficient divisors)
| Project/Area Number |
10640196
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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, Associate Professor, 教養科, 助教授 (60175718)
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| Co-Investigator(Kenkyū-buntansha) |
KAMADA Hiroyuki Numazu College of Technology, Division of Liberal Arts, Assistant Professor, 教養科, 講師 (00249799)
MACHIDA Yoshinori Numazu College of Technology, Division of Liberal Arts, Associate Professor, 教養科, 助教授 (90141895)
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| Project Period (FY) |
1998 – 1999
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| Keywords | meromorphic map / unicity theorem / algebraic dependence / Nevanlinna's deficient divisor / finiteness theorem |
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| Research Abstract |
The head investigator Aihara has studied the uniqueness problem of meromorphic mappings. He proved finiteness theorems for some families of meromorphic mappings (Osaka Math. J. 35 (1998)), and proved some unicity theorems for dominant meromorphic mappings into a projective algebraic manifold under conditions on deficiencies (Tohoku Math. J. 51 (1999)). He also dealt with the case where meromorphic mappings into complex projective spaces with hyperplanes as divisors (to appear in Complex Variables 41 (2000)). Furthermore, he has investigated the propagation of algebraic dependence of meromorphic mappings. He gave some criteria for dependence of meromorphic mappings from finite sheeted analytic covering spaces over the complex m-space into a projective algebraic manifold and their applications (Algebraic dependence in value distribution theory, preprint, 2000). In particular, he gave a condition that two holomorphic mappings into a smooth elliptic curve are algebraically related by endomorphisms of elliptic curve.
An investigator Machida studied decomposable Monge-Ampere equations. An investigator Kamada studied a neutral hyperkahler structure on a primary Kodaira surface. He also studied an almost Hermitian Einstein-Weyl structure on a compact four-dimensional manifold, and proved some integrability results of almost complex structure under a suitable curvature condition.
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