Degenerate problem with truncated multiplicities of two meromorphic mappings on a K\"{a}hler manifold

Abstract

Let $\M$ be a complete K\"{a}hler manifold whose universal covering is biholomorphic to a ball $B^m(R_0)\ (0<R_0\le +\infty)$ in $\C^m$. In this paper, we give a generation for the algebraic problem of two meromorphic mappings from $\M$ into $\P^n(\C)$. We succeed in proving the degenerate theorem that the truncated levels vary along hyperplanes and we also reduce the levels of truncation compared with the previous ones.