Two meromorphic mappings sharing 2n+2 hyperplanes regardless of multiplicity

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:410

Article

Si Duc Quang¹  Le Ngoc Quynh² 

[1] Hanoi Natl Univ Educ, Dept Math, Hanoi, Vietnam

[2] An Giang Univ, Fac Educ, Long Xuyen, An Giang, Vietnam

关键词: Degenerate;    Meromorphic mapping;    Truncated multiplicity;    Hyperplane;   

DOI  :  10.1016/j.jmaa.2013.09.003

来源: Elsevier

【 摘 要 】

Nevanlinna showed that two non-constant meromorphic functions on C must be linked by a Mobius transformation if they have the same inverse images counted with multiplicities for four distinct values. After that this result is generalized by Gundersen to the case where two meromorphic functions share two values ignoring multiplicity and share other two values with multiplicities truncated by 2. Previously, the first author proved that for n >= 2, there are at most two linearly non-degenerate meromorphic mappings of C-m into P-n(C) sharing 2n + 2 hyperplanes ingeneral position ignoring multiplicity. In this article, we will show that if two meromorphic mappings f and g of C-m into P-n(C) share 2n + 1 hyperplanes ignoring multiplicity and another hyperplane with multiplicities truncated by n + 1 then the map f x g is algebraically degenerate. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free