A note on Fujimoto's uniqueness theorem with (2n+3) hyperplanes

2023/07/31 by Zhou, Kai
#20K15 #32H30 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2307.16595

Abstract

Hirotaka Fujimoto proved in [Nagoya Math. J., 1976(64): 117--147] and [Nagoya Math. J., 1978(71): 13--24] a uniqueness theorem for algebraically non-degenerate meromorphic maps into ℙⁿ(ℂ) sharing (2n+3) hyperplanes in general position. The proof of Lemma 3.6 in [Nagoya Math. J., 1976(64): 117--147] is found to contain a mistake. This mistake can be corrected easily from a new point of view. This note explains the idea of the correction and provides a complete proof.

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