scholarly journals Uniqueness Problem for Meromorphic Mappings with Truncated Multiplicities and Moving Targets

2006 ◽  
Vol 181 ◽  
pp. 75-101 ◽  
Author(s):  
Gerd Dethloff ◽  
Tran Van Tan
Keyword(s):  
Uniqueness Theorem ◽  
Distribution Theory ◽  
Value Distribution ◽  
Uniqueness Problem ◽  
Moving Targets ◽  
Value Distribution Theory ◽  
Meromorphic Mappings

AbstractIn this paper, using techniques of value distribution theory, we give a uniqueness theorem for meromorphic mappings of ℙm into ℙPn with (3n+1) moving targets and truncated multiplicities.

scholarly journals Uniqueness problem with truncated multiplicities in value distribution theory

1998 ◽  
Vol 152 ◽  
pp. 131-152 ◽  
Author(s):  
Hirotaka Fujimoto
Keyword(s):  
General Position ◽  
Meromorphic Functions ◽  
Distribution Theory ◽  
Value Distribution ◽  
Uniqueness Problem ◽  
Value Distribution Theory ◽  
Meromorphic Maps

Abstract.In 1929, H. Cartan declared that there are at most two meromorphic functions on ℂ which share four values without multiplicities, which is incorrect but affirmative if they share four values counted with multiplicities truncated by two. In this paper, we generalize such a restricted H. Cartan’s declaration to the case of maps into PN (ℂ). We show that there are at most two nondegenerate meromorphic maps of ℂn into PN(ℂ) which share 3N + 1 hyperplanes in general position counted with multiplicities truncated by two. We also give some degeneracy theorems of meromorphic maps into PN (ℂ) and discuss some other related subjects.

scholarly journals Uniqueness problem with truncated multiplicities in value distribution theory, II

1999 ◽  
Vol 155 ◽  
pp. 161-188 ◽  
Author(s):  
Hirotaka Fujimoto
Keyword(s):  
General Position ◽  
Distribution Theory ◽  
Value Distribution ◽  
Uniqueness Problem ◽  
Value Distribution Theory ◽  
Meromorphic Maps

AbstractLet H1, H2,…,Hq be hyperplanes in PN (ℂ) in general position. Previously, the author proved that, in the case where q ≥ 2N + 3, the condition ν(f,Hj) = ν(g, Hj) imply f = g for algebraically nondegenerate meromorphic maps f, g: ℂn → PN(ℂ), where ν(f, Hj) denote the pull-backs of Hj through f considered as divisors. In this connection, it is shown that, for q ≥ 2N + 2, there is some integer ℓ0 such that, for any two nondegenerate meromorphic maps f, g: ℂn → PN(ℂ) with min(ν(f, Hj),ℓ0) = min(ν(g, Hj), ℓ0) the map f × g into PN(ℂ) × PN(ℂ) is algebraically degenerate. He also shows that, for N = 2 and q = 7, there is some ℓ0 such that the conditions min(ν(f, Hj), ℓ0) = min(ν(g, Hj), ℓ0) imply f = g for any two nondegenerate meromorphic maps f, g into P2(ℂ) and seven generic hyperplanes Hj’s.

scholarly journals Algebraic dependence of meromorphic mappings in value distribution theory

2003 ◽  
Vol 169 ◽  
pp. 145-178 ◽  
Author(s):  
Yoshihiro Aihara
Keyword(s):  
Elliptic Curve ◽  
Value Distribution ◽  
Holomorphic Mappings ◽  
Covering Space ◽  
Uniqueness Problem ◽  
Algebraic Manifold ◽  
Finite Covering ◽  
Value Distribution Theory ◽  
Algebraic Dependence ◽  
Meromorphic Mappings

AbstractIn this paper we first prove some criteria for the propagation of algebraic dependence of dominant meromorphic mappings from an analytic finite covering space X over the complex m-space into a projective algebraic manifold. We study this problem under a condition on the existence of meromorphic mappings separating the generic fibers of X. We next give applications of these criteria to the uniqueness problem of meromorphic mappings. We deduce unicity theorems for meromorphic mappings and also give some other applications. In particular, we study holomorphic mappings into a smooth elliptic curve E and give conditions under which two holomorphic mappings from X into E are algebraically related.

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