Let f and g be two holomorphic curves of a ball Δ(R)\documentclass[12pt]{minimal}
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\begin{document}$$\Delta (R)$$\end{document} into Pn(C)\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {P}}^n({\mathbb {C}})$$\end{document} with finite growth index, and let H1,…,H2n+2\documentclass[12pt]{minimal}
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\begin{document}$$H_1,\ldots ,H_{2n+2}$$\end{document} be 2n+2\documentclass[12pt]{minimal}
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\begin{document}$$2n+2$$\end{document} hyperplanes in general position. In this paper, our first purpose is to show that if f and g have the same inverse images for all Hi(1≤i≤2n+2)\documentclass[12pt]{minimal}
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\begin{document}$$H_i\ (1\le i\le 2n+2)$$\end{document} with multiplicities counted to level li\documentclass[12pt]{minimal}
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\begin{document}$$l_i$$\end{document} satisfying an explicitly estimate concerning cf\documentclass[12pt]{minimal}
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\begin{document}$$c_f$$\end{document} and cg\documentclass[12pt]{minimal}
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\begin{document}$$c_g$$\end{document}, then the map f×g\documentclass[12pt]{minimal}
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\begin{document}$$f\times g$$\end{document} into Pn(C)×Pn(C)\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {P}}^n({\mathbb {C}})\times {\mathbb {P}}^n({\mathbb {C}})$$\end{document} must be algebraically degenerated. Our second purpose is to prove that f=g\documentclass[12pt]{minimal}
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\begin{document}$$f=g$$\end{document} if they share 2n+2\documentclass[12pt]{minimal}
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\begin{document}$$2n+2$$\end{document} hyperplanes with some certain conditions (in particular, they share 2n+2\documentclass[12pt]{minimal}
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\begin{document}$$2n+2$$\end{document} hyperplanes with multiplicities counted to level n+1\documentclass[12pt]{minimal}
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\begin{document}$$n+1$$\end{document}). Our results extend and improve the previous results for the case of holomorphic curve from C\documentclass[12pt]{minimal}
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\begin{document}$${\mathbb {C}}$$\end{document} on these directions.
