Uniqueness Theorems for Meromorphic Mappings with Few Targets
Complex Variables
2014-12-01 v1 Algebraic Geometry
Abstract
The purpose of this article is to show uniqueness theorems for meromorphic mappings of C^m to CP^n with few hyperplanes H_j, j=1,...,q. It is well known that uniqueness theorems hold for q \geq 3n+2. In this paper we show that for every nonnegative integer c there exists a positive integer N(c), depending only on c in an explicit way, such that uniqueness theorems hold if q\geq (3n+2 -c) and n\geq N(c). Furthermore, we also show that the coefficient of n in the formula of q can be replaced by a number which is strictly smaller than 3 for all n>>0. At the same time, a big number of recent uniqueness theorems are generalized considerably.
Cite
@article{arxiv.0711.1720,
title = {Uniqueness Theorems for Meromorphic Mappings with Few Targets},
author = {Gerd Dethloff and Tran Van Tan},
journal= {arXiv preprint arXiv:0711.1720},
year = {2014}
}