Algebraic dependence of meromorphic mappings in value distribution theory
Algebraic dependence of meromorphic mappings in value distribution theory
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DOI：
10.1017/s0027763000008473
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发表时间：
2003
影响因子：
0.8
通讯作者：
Yoshihiro Aihara
中科院分区：
文献类型：
--
作者：
Yoshihiro Aihara
摘要本文首先证明了支配亚纯映射的代数依赖从复m-空间上的解析有限覆盖空间X传播到射影代数流形的一些准则。我们在存在分离X的一般纤维的亚纯映射的条件下研究了这个问题。其次，我们将这些准则应用于亚纯映射的唯一性问题。给出了亚纯映射的唯一性定理，并给出了一些应用。特别地，我们研究了到光滑椭圆曲线E上的全纯映射，给出了从X到E的两个全纯映射代数相关的条件。
Abstract In this paper we first prove some criteria for the propagation of algebraic dependence of dominant meromorphic mappings from an analytic finite covering space X over the complex m-space into a projective algebraic manifold. We study this problem under a condition on the existence of meromorphic mappings separating the generic fibers of X. We next give applications of these criteria to the uniqueness problem of meromorphic mappings. We deduce unicity theorems for meromorphic mappings and also give some other applications. In particular, we study holomorphic mappings into a smooth elliptic curve E and give conditions under which two holomorphic mappings from X into E are algebraically related.