Second main theorems for meromorphic mappings intersecting moving hyperplanes with truncated counting functions and unicity problem (Q266529)

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scientific article; zbMATH DE number 6568128
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Second main theorems for meromorphic mappings intersecting moving hyperplanes with truncated counting functions and unicity problem
scientific article; zbMATH DE number 6568128

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    Second main theorems for meromorphic mappings intersecting moving hyperplanes with truncated counting functions and unicity problem (English)
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    13 April 2016
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    The paper deals with inequalities of second main theorem type for meromorphic mappings and for moving targets. Let \(f:{\mathbb C}^m \to {\mathbb P}^n({\mathbb C})\) be a meromorphic mapping and \(\{a_j\}_{j=1}^q\) moving hyperplanes in general position in \({\mathbb P}^n({\mathbb C})\). We let \(\mathrm{rank} (f)\) denote the rank of the set \(\{f_0,\ldots,f_n\}\) over the field generated by \(\{a_j\}\), where \(f=(f_0,\ldots,f_n)\) is a reduced representation of \(f\). Assume that \((f, a_j)\not\equiv 0\) and \(q > 2n-k+2\), where \(k=\mathrm{rank} (f)\). Then the author proves the following: \[ \frac{q}{2n-k+2} T_f(r) \leq \sum_{j=1}^q N^{[k]}_{(f, a_j)}(r) +o(T_ f(r))+ O(\max T_{a_j}(r)). \] He also gives a unicity theorem as an application of the above result.
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    meromorphic mappings
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    second main theorem
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    moving targets
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    unicity theorem
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