Project/Area Number  10640196 
Research Category 
GrantinAid for Scientific Research (C).

Section  一般 
Research Field 
Basic analysis

Research Institution  Numazu College of Technology 
Principal Investigator 
AIHARA Yoshihiro Numazu College of Technology, Division of Liberal Arts, Associate Professor, 教養科, 助教授 (60175718)

CoInvestigator(Kenkyūbuntansha) 
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)

Project Fiscal Year 
1998 – 1999

Project Status 
Completed(Fiscal Year 1999)

Budget Amount *help 
¥2,600,000 (Direct Cost : ¥2,600,000)
Fiscal Year 1999 : ¥1,200,000 (Direct Cost : ¥1,200,000)
Fiscal Year 1998 : ¥1,400,000 (Direct Cost : ¥1,400,000)

Keywords  meromorphic map / unicity theorem / algebraic dependence / Nevanlinna's deficient divisor / finiteness theorem / 有理型写像 / 一意性問題 / 代数的従属性 / ネヴァンリンナの除外値 / 有限性定理 
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 mspace 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 MongeAmpere equations. An investigator Kamada studied a neutral hyperkahler structure on a primary Kodaira surface. He also studied an almost Hermitian EinsteinWeyl structure on a compact fourdimensional manifold, and proved some integrability results of almost complex structure under a suitable curvature condition.
