Let f, g be linearly nondegenerate meromorphic mappings of C^m into C Pⁿ. Let {H_j}_{j = 1}^q be hyperplanes in C Pⁿ in general position, such that. (a)f^{- 1} (H_j) = g^{- 1} (H_j), for all 1 ≤ j ≤ q,(b)dim (f^{- 1} (H_i) ∩ f^{- 1} (H_j)) ≤ m - 2 for all 1 ≤ i < j ≤ q, and(c)f = g on {n-ary union}_{j = 1}^q f^{- 1} (H_j). 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.

Dethloff G., Tan T.V.

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