A new version of the second main theorem for meromorphic mappings intersecting hyperplanes in several complex variables

Abstract

Let $c\in {\mathbb{C}}^m,$ $f:{\mathbb{C}}^m\to {\mathbb{P}}^n(\mathbb{C})$ be a linearly nondegenerate meromorphic mapping over the field ${\mathcal{P}}_c$ of $c$-periodic meromorphic functions in ${\mathbb{C}}^m$, and let $H_j$ $(1\le j\le q)$ be $q(>2N-n+1)$ hyperplanes in $N$-subgeneral position of ${\mathbb{P}}^n(\mathbb{C}).$ We prove a new version of the second main theorem for meromorphic mappings of hyperorder strictly less than one without truncated multiplicity by considering the Casorati determinant of $f$ instead of its Wronskian determinant. As its applications, we obtain a defect relation, a uniqueness theorem and a difference analogue of generalized Picard theorem.

27 pages