A proof of the generalized Picard's little theorem using matrices (Q1345511)
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scientific article; zbMATH DE number 731879
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A proof of the generalized Picard's little theorem using matrices |
scientific article; zbMATH DE number 731879 |
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A proof of the generalized Picard's little theorem using matrices (English)
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8 March 1995
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Let \(\mathbb{P}_n\) be the \(n\)-dimensional complex projective space. The generalized Picard's Little Theorem is known as follows: If a holomorphic map \(f : \mathbb{C}^m \to \mathbb{P}_n \subset \mathbb{P}_N\) is nondegenerate, then it omits at most \(N + [N/n]\) hyperplanes of \(\mathbb{P}_N\) in general position, where \(n \geq 1\). This theorem is proved again in this paper by using linear algebra technique via argument of matrices.
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matrix technique
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complex projective space
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Picard's Little Theorem
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holomorphic map
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