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

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 algebraic degeneracy of holomorphic curves on \({\cal P}_c^1\) 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. Our second main theorem and difference analogue of Picard’s theorem recover the results of Cao-Korhonen [1] and Halburd-Korhonen-Tohge [8], respectively. By a way, we also obtain uniqueness theorems of meromorphic mappings which improve the result of Dulock-Ru [4].