CÁC BÀI BÁO KHOA HỌC 16:32:03 Ngày 16/10/2019 GMT+7
Uniqueness theorems for meromorphic mappings with few hyperplanes

Let f, g be linearly nondegenerate meromorphic mappings of Cm into C Pn. Let {Hj}j = 1q be hyperplanes in C Pn in general position, such that. (a)f- 1 (Hj) = g- 1 (Hj), for all 1 ≤ j ≤ q,(b)dim (f- 1 (Hi) ∩ f- 1 (Hj)) ≤ m - 2 for all 1 ≤ i < j ≤ q, and(c)f = g on {n-ary union}j = 1q f- 1 (Hj). It is well known that if q ≥ 3 n + 2, then f ≡ g. In this paper we show that for every nonnegative integer c there exists positive integer N (c) depending only on c in an explicit way such that the above result remains valid if q ≥ (3 n + 2 - c) and n ≥ 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. © 2008 Elsevier Masson SAS. All rights reserved.

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