# Difference analogue of second main theorems for meromorphic mapping into algebraic variety

## TL;DR

This paper develops difference analogues of second main theorems for meromorphic mappings into algebraic varieties, extending classical value distribution theory to difference settings and applications to uniqueness and degeneracy of holomorphic curves.

## Contribution

It introduces difference analogues of second main theorems for meromorphic mappings into algebraic varieties, including results on degeneracy, Picard-type theorems, and uniqueness sharing hypersurfaces.

## Key findings

- Established difference second main theorems for meromorphic mappings.
- Proved algebraic degeneracy results for holomorphic curves intersecting hypersurfaces.
- Derived a difference analogue of Picard's theorem and uniqueness theorems.

## Abstract

In this paper, we prove some difference analogue of second main theorems of meromorphic mapping from Cm into an algebraic variety V intersecting a finite set of fixed hypersurfaces in subgeneral position. As an application, we prove a result on algebraically degenerate of holomorphic curves intersecting hypersurfaces and difference analogue of Picard's theorem on holomorphic curves. Furthermore, we obtain a second main theorem of meromorphic mappings intersecting hypersurfaces in N-subgeneral position for Veronese embedding in Pn(C) and a uniqueness theorem sharing hypersurfaces.