Construction of hyperbolic hypersurfaces of low degree in \(\mathbb{P}^n(\mathbb{C})\) (Q2816969)
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scientific article; zbMATH DE number 6619851
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Construction of hyperbolic hypersurfaces of low degree in \(\mathbb{P}^n(\mathbb{C})\) |
scientific article; zbMATH DE number 6619851 |
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26 August 2016
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Kobayashi conjecture
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hyperbolicity
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Brody lemma
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Nevanlinna theory
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Construction of hyperbolic hypersurfaces of low degree in \(\mathbb{P}^n(\mathbb{C})\) (English)
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The article under review gives a new construction for obtaining low degree hyperbolic hypersurfaces \(X_d \subset \mathbb{P}^{n+1}(\mathbb{C})\) for arbitrary~\(n\).NEWLINENEWLINEWhile previously such constructions were only known if the degree \(d\) was at least \(4n^2\) asymptotically, the author obtains families of hyperbolic degree-\(d\) hypersurfaces \(X_d \subset \mathbb{P}^{n+1}(\mathbb{C})\) for any \(d \geq (\frac{n+3}{2})^2\).NEWLINENEWLINEThe constructed hypersurfaces are given by small deformations of a union of \(d\) hyperplanes in general position.
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