Meromorphic mappings into projective varieties intersecting arbitrary families of moving hypersurfaces

Abstract

In this paper, we establish a general second main theorem for meromorphic mappings from ${\mathbb{C}}^m$ into a subvariety $V$ of ${\mathbb{P}}^n(\mathbb{C})$ with respect to an arbitrary family of slowly moving hypersurfaces $\mathcal{Q}=\{Q_1,\dots ,Q_q\}$. In contrast to the usual setting, the mapping is not required to be algebraically nondegenerate over the field ${\mathcal{K}}_{\mathcal{Q}}$. Moreover, the truncation levels of the counting functions are explicitly estimated, and the total defect bound is given by $\hat{I}{”}_{\mathcal{Q},V}(3\dim V-1)$, which is independent of the mapping $f$, where $\hat{I}{”}_{\mathcal{Q},V}$ denotes the distributive constant of $\mathcal{Q}$ with respect to $V$.

20 pages