ON CARTANS THEOREM AND CARTANS CONJECTURE

We give a mild generalization of Cartan's theorem on value distributio n for a holomorphic curve in projective space relative to hyperplanes. This generalization is used to complete the proof of the following th eorem claimed in an earlier paper by the author: Given hyperplanes in projective space in general position, there exists a finite union of p roper linear subspaces such that all holomorphic curves not contained in that union (even linearly degenerate curves) satisfy the inequality of Cartan's theorem, except for the ramification term. In addition, i t is shown how these methods can lead to a shorter proof of Nochka's t heorem on Cartan's conjecture and (in the number field case) how Nochk a's theorem gives a short proof of Wirsing's theorem on approximation of algebraic numbers by algebraic numbers of bounded degree.