论文标题
代数依赖性和有限性问题，在Kähler歧管上差异化非排效性映射
Algebraic dependence and finiteness problems of differentiably nondegenerate meromorphic mappings on Kähler manifolds
论文作者
论文摘要
让$ m $成为一个完整的kähler歧管，其通用覆盖物是$ \ mathbb b^m（r_0）$ in $ \ mathbb c^m $（$ 0 <r_0 \ le +\ le +\ infty $）。本文我们的第一个目的是研究差异化映射的代数依赖性问题。我们将表明，如果$ k $差异性不重新呈杂种映射$ f^1，\ ldots，\ ldots，f^k $ $ m $ of $ m $中的$ \ m artbb p^n（\ m m缩c）\（n \ ge 2）$满足条件$（c_p）$的$（c_ρ）$，然后在$ supeneral cot wed unterplan中的$（c_ pegge wed）$ supeneral cot f. f^k \ equiv 0 $。为了第二个目的，我们将证明，最多有两个不同的非成绩映射，将$ m $ $ m $的非成型映射到$ \ mathbb p^n（\ mathbb c）$共享$ q \（q \ sim 2n-n+3+3+3+3+o（ρ））$ subseral subteneral位置中的$ spretplanes $ subteneral位置的$。我们的结果概括了以前的有限性和独特性定理，用于$ \ mathbb c^m $的不同Meromormormormormormorphic映射，并扩展了Kähler歧管映射的情况下的一些先前结果。
Let $M$ be a complete Kähler manifold, whose universal covering is biholomorphic to a ball $\mathbb B^m(R_0)$ in $\mathbb C^m$ ($0<R_0\le +\infty$). Our first aim in this paper is to study the algebraic dependence problem of differentiably meromorphic mappings. We will show that if $k$ differentibility nondegenerate meromorphic mappings $f^1,\ldots,f^k$ of $M$ into $\mathbb P^n(\mathbb C)\ (n\ge 2)$ satisfying the condition $(C_ρ)$ and sharing few hyperplanes in subgeneral position regardless of multiplicity then $f^1\wedge\cdots\wedge f^k\equiv 0$. For the second aim, we will show that there are at most two different differentiably nondegenerate meromorphic mappings of $M$ into $\mathbb P^n(\mathbb C)$ sharing $q\ (q\sim 2N-n+3+O(ρ))$ hyperplanes in $N-$subgeneral position regardless of multiplicity. Our results generalize previous finiteness and uniqueness theorems for differentiably meromorphic mappings of $\mathbb C^m$ and extend some previous results for the case of mappings on Kähler manifold.
