On the deficiency of holomorphic curves with maximal deficiency sum (Q5940263)

The author proves the following result: Let \(f:\mathbb{C}\rightarrow \mathbb{P}^n(\mathbb{C})\) be a linearly non-degenerate, transcendental holomorphic curve. Let \(X\) be a subset of \(\mathbb{C}^{n+1}-\{0\}\) in \(N\)-subgeneral position. Assume that \(f\) has a maximal deficiency sum, that is, the defect relation NEWLINE\[NEWLINE\sum_{a\in X}\delta(a,f)=2N-n+1NEWLINE\]NEWLINE holds. If \((n+1,2N-n+1)=1\), then there are at least NEWLINE\[NEWLINE\left[\frac{2N-n+1}{n+1}\right]+1NEWLINE\]NEWLINE vectors \(a\in X\) satisfying \(\delta(a,f)=1\).