Two meromorphic mappings having the same inverse images of some moving hyperplanes with truncated multiplicity

Abstract

Let $f$ and $g$ be two meromorphic mappings of ${ℂ}^m$ into ${\mathbb{P}}^n(ℂ)$ and let $a_1,\dots ,a_{2n+2}$ be $2n+2$ moving hyperplanes which are slow with respect to $f$ and $g$. We will show that if $f$ and $g$ have the same inverse images for all $a_i(1\le i\le 2n+2)$ with multiplicities counted to level $l_i$ such that

where $q=\left(\genfrac{}{}{0.0pt}{}{2n+2}{n+1}\right)$, then the map $f\times g$ into ${\mathbb{P}}^n(ℂ)\times {\mathbb{P}}^n(ℂ)$ must be algebraically degenerate over the field ${\mathcal{ℛ}}_{{\{a_i\}}_{i=1}^{2n+2}}$. Our result extends and improves the previous result in this topic.