Equidistribution theory in higher dimensions

Chia-Chi Tung

Vol. 78 (1978), No. 2, 525–548

DOI: 10.2140/pjm.1978.78.525

Abstract

Let X, Y be complex spaces, and f : X ⇁ Y a meromorphic map. Assume in Y an admissible family A = {S_b}_b∈N of analytic subsets S_b is given. Assume f is almost adapted to A. The purpose of this paper is to prove that, if f satisfies certain growth conditions, the valence of S_b (for almost all S_b ∈ A) grows to infinity at the same rate as the characteristic of f. Here X is assumed to carry an exhaustion function which is, e.g., g-concave, centrally g-convex or g-quasiparabolic.

Mathematical Subject Classification 2000

Primary: 32H30

Milestones

Received: 15 November 1977

Published: 1 October 1978