On the value distribution of meromorphic mappings (the uniqueness problem and the existence problem of deficient divisors)

首席研究员Aihara研究了亚纯映射的唯一性问题。他证明了一些亚纯映射族的有限定理(Osaka Math.J.35(1998))，并在亏量条件下证明了占优亚纯映射到射影代数流形的一些唯一性定理(东北数学。J.51(1999))。他还讨论了亚纯映射到以超平面为因子的复射影空间的情况(出现在复变量41(2000)中)。此外，他还研究了亚纯映射的代数相依性的传播。他给出了从复m-空间上的有限张解析覆盖空间到射影代数流形的亚纯映射依赖的一些判据及其应用(《值分布理论中的代数依赖》，Preprint，2000)。特别地，他给出了光滑椭圆曲线上的两个全纯映射通过椭圆曲线的自同态代数相关的条件。一名研究人员Kamada研究了初级Kodaira表面上的中性Hyperkahler结构。他还研究了紧致四维流形上的几乎Hermite Einstein-Weyl结构，并在适当的曲率条件下证明了几乎复结构的可积性结果。

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.