In this paper, we will show that if two meromorphic mappings $f$ and $g$ of $\mathbb C^m$ into $\mathbb P^n(\mathbb C)$ have the same inverse images for $(2n+2)$ moving hyperplanes $\{ a_i\}_{ i=1}^{ 2n+2}$ with multiplicities counted to level $l_0$ then the map $f\times g$ must be algebraically degenerated over the field $\mathcal R\{ a_i\}_{ i=1}^{ 2n+2}$, where $l_0=3n^3(n+1)q(q-2)$ with $q=\binom{ 2n+2}{ n+2}$. Our result generalizes the previous result for fixed hyperplanes case of Fujimoto and also improves his result by giving an explicit estimate for the number $l_0$.
Categories: math.CV