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

Abstract

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 $f^{\ast }(H_j)=g^{\ast }(H_j)$ $(1\le j\le 2n+2)$ 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.

arXiv admin note: substantial text overlap with arXiv:2308.01106