Uniqueness problem without multiplicities in value distribution theory

Shanyu Ji

Vol. 135 (1988), No. 2, 323–348

DOI: 10.2140/pjm.1988.135.323

Abstract

Let H₁,…,H_k be hyperplanes in general position in P^m with m ≥ 2. Let A₁,…,A_k be pure (n − 1)-dimensional analytic subsets of Cⁿ with codim A_i ∩ A_j ≥ 2 whenever i≠j. Then any linearly non-degenerate meromorphic maps f,g,h : Cⁿ → P^m with f|A_j = g|A_j = h|A_j and with f⁻¹(H_j) = g⁻¹(H_j) = h⁻¹(H_j) = A_j for j = 1,…,k satisfy Property (P) if k = 3m + 1. Consequently such f, g, h are algebraically dependent. If even n ≥ rank f = rank g = rank h = m, then k = m + 3 suffices.

Mathematical Subject Classification 2000

Primary: 32H30

Milestones

Received: 13 April 1987

Published: 1 December 1988