A uniqueness theorem for meromorphic maps into $\mathbb{P}^n$ with generic $(2n+2)$ hyperplanes

Let $H_1,\dots,H_{2n+2}$ be \emph{generic} $(2n+2)$ hyperplanes in $\mathbb{P}^n.$ It is proved that if meromorphic maps $f$ and $g$ of $\mathbb{C}^m$ into $\mathbb{P}^n$ satisfy $f^*(H_j)=g^*(H_j)$ $(1\leq j\leq 2n+2)$ and $g$ is algebraically non-degenerate then $f=g.$ This result is essentially implied by the proof of Hirotaka Fujimoto in papers [Nagoya Math. J., 1976(64): 117--147] and [Nagoya Math. J., 1978(71): 13--24]. This note gives a complete proof of the above uniqueness result.