The uniqueness problem for meromorphic mappings with truncated multiplicities
The uniqueness problem for meromorphic mappings with truncated multiplicities
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DOI：
10.2996/kmj/1352985450
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发表时间：
2012-10
影响因子：
0.6
通讯作者：
F. Lü
中科院分区：
文献类型：
--
作者：
F. Lü
这项工作的目的是双重的。第一个问题是解决T。Cao和H. Yi在[1]中。第二是推广了Z.陈和M. Ru [2]，Z. Chen和Q. Yan [3]，D. Thai和S. Quang [13]. 1.超平面的唯一性问题1926年R. Nevanlinna [10]证明了如果两个亚纯函数对于五个不同的值有相同的逆像，那么这两个函数一定是相同的。1975年，H. Nevanlinna的结果被推广到了C到P_∞ C_∞的亚纯映射的情形。Fujimoto [6].事实上，他得到了：对于C到PdC中的两个线性非退化亚纯映射f和g，如果它们在PdC中的一般位置上对3n^2个超平面具有相同的重数逆象，则f 1/4 g。在过去的几十年里，已经有很多关于这个问题的结果。(see H. Fujimoto [7]，S. Ji [9]，M. Ru [11]，Z. Chen和Q. Yan [15]）设f是C到P_∞ C_∞的线性非退化亚纯映射.对于每个超平面H，我们用vf; Hc表示C到N 0的映射，使得vf; Hc; Hc（a A C）是f和H在f的像的交重数。取q个超平面H1;。. . ;Hq在一般位置上的Pmccq和正整数l0。考虑所有线性非退化亚纯映射g：C的族fHjg j1/41; f ; l0！符合条件的考生：2000年数学学科分类485。32点30分30点35分
The purpose of this work is twofold. The first is to solve a uniqueness problem of meromorphic mappings posed by T. Cao and H. Yi in [1]. The second is to generalize several previous uniqueness theorems of meromorphic mappings ‘‘partially’’ sharing a few moving targets, which were given by Z. Chen and M. Ru [2], Z. Chen and Q. Yan [3], D. Thai and S. Quang [13]. 1. The uniqueness problem for hyperplanes In 1926, R. Nevanlinna [10] showed that if two meromorphic functions have the same inverse images for five distinct values, then these two functions must be identical. In 1975, the Nevanlinna’s result was generalized to the case of meromorphic mappings of C into PðCÞ by H. Fujimoto [6]. In fact, he obtained that for two linearly non-degenerate meromorphic mappings f and g of C into PðCÞ, if they have the same inverse images counted with multiplicities for 3nþ 2 hyperplanes in general position in PðCÞ, then f 1⁄4 g. Over the last few decades, there have been a lot of results related this problem. (see H. Fujimoto [7], S. Ji [9], M. Ru [11], Z. Chen and Q. Yan [15]) Let f be a linearly non-degenerate meromorphic mapping of C into PðCÞ. For each hyperplane H we denote by vð f ;HÞ the map of C into N0 such that vð f ;HÞðaÞ (a A C) is the intersection multiplicity of the image of f and H at f ðaÞ. Take q hyperplanes H1; . . . ;Hq in PðCÞ in general position and a positive integer l0. Consider the family FamðfHjg j1⁄41; f ; l0Þ of all linearly non-degenerate meromorphic mappings g : C ! PðCÞ satisfying the conditions: 485 2000 Mathematics Subject Classification. 32H30, 30D35.