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 $\mathcal Q=\{Q_1,\ldots,Q_q\}$. 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 $Δ_{\mathcal Q,V}(3\dim V-1)$, which is independent of the mapping $f$, where $Δ_{\mathcal Q,V}$ denotes the distributive constant of $\mathcal Q$ with respect to $V$.