A NOTE ON UNIQUENESS PROBLEM FOR HOLOMORPHIC CURVES WITH HYPERSURFACES

Abstract

Recently, several uniqueness theorems for holomorphic curves on an annulus have been published. For example, in 2013, H. T. Phuong and T. H. Minh given two uniqueness results with hyperplanes in general position. In 2021, H. T. Phuong and L. Vilaisavanh proved some uniqueness theorems for the holomorphic mappings on an annulus sharing hypersurfaces in general position or hypersurfaces in general position for Veronese embedding. In this paper, we consider the same problem in the case of hypersurfaces in general position by using the second main theorem for holomorphic curves on an annulus with hypersurfaces. The main result of the paper is Theorem 1, which gives us an algebraic condition so that two holomorphic curves on an annulus are equal. The main technique in the paper is based on a form of the second fundamental theorem for holomorphic curve on an annulus with target being hypersurfaces and some other techniques in Nevanlinna-Cartan theory.