Another proof of the defect relation for moving targets (Q1188483)

Let \(f:\mathbb{C}\to P^ n(\mathbb{C})\) be a holomorphic mapping with reduced representation \(\tilde f=(f_ 0,\dots,f_ n)\) and \(\tilde g_ j(0\leq j\leq q)\) be holomorphic mappings of the same kind such that (i) \(T(g_ j;r)=O(T(f;r))\) (ii) \(g_ j(0\leq j\leq q)\) are in general position (iii) \(f\) is non-degenerate over the field \({\mathcal K}\) generated by the quotients \(g_{jk}/g_{j0}\). Then the generalized defect relation \(\sum^ q_{j=0}\delta(f,g_ j)\leq n+1\) holds. This was proved for the first time by Ru and Stoll. In the present paper a simpler proof is given which is close to the one- dimensional proof due to the reviewer.