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

首席研究员相原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性定理（Osaka Math. J. 35 (1998)），并证明了在缺陷条件下主导亚纯映射到射影代数流形的一些唯一性定理（Tohoku Math. J. 51 (1999)）。他还处理了亚纯映射到以超平面作为除数的复射影空间的情况（出现在 Complex Variables 41 (2000) 中）。此外，他还研究了亚纯映射的代数依赖性的传播。他给出了从复杂 m 空间上的有限片解析覆盖空间到射影代数流形的亚纯映射依赖性的一些标准及其应用（值分布理论中的代数依赖性，预印本，2000）。特别是，他给出了一个条件，即光滑椭圆曲线的两个全纯映射通过椭圆曲线的自同态在代数上相关。 一位研究者 Machida 研究了可分解的 Monge-Ampere 方程。镰田研究员研究了小平初级表面上的中性超卡勒结构。他还研究了紧四维流形上的近厄米爱因斯坦-外尔结构，并证明了在适当曲率条件下近复结构的一些可积性结果。

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.