Uniqueness problem of meromorphic mappings from a complete K\"{a}hler manifold into a projective variety

TL;DR

This paper establishes new unicity theorems for meromorphic mappings from complete Kähler manifolds into projective varieties, focusing on shared hypersurfaces and hyperplanes, advancing the understanding of their uniqueness properties.

Contribution

It proves novel unicity theorems for meromorphic mappings sharing hypersurfaces and hyperplanes, extending previous results to broader geometric contexts.

Findings

Unicity theorem for mappings sharing few hypersurfaces

Unicity theorem for differential nondegenerate mappings sharing hyperplanes

Extension of unicity results to subgeneral position hyperplanes

Abstract

The purpose of this paper has twofold. The first is to prove a unicity theorem for meromorphic mappings of a complete K\"{a}hler manifold M in P^n(C) sharing few hypersurfaces. The second is to give a unicity theorem for the case of differential nondegenerate meromorphic mappings sharing 2N-n+3+2\rho(2N-n+1) hyperplanes in N subgeneral position.