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The complement to \(2n\) hyperplanes in \(\mathbb{CP}^ n\) is not hyperbolic. (Russian) Zbl 0611.51019
The main result of the paper is the following. Let \(k\) be a field and \(\text{card}(k)\geq 2n\). For every choice of \(2n\) hyperplanes \(\{D_ i\}^{2n}_{i=1}\) of \(k{\mathbb P}^ n\), there is a line \(q\) such that \(| (\cup^{2n}_{i=1}D_ i)\cap q| \leq 2\). Thus it is verified the hypothesis of P. Kiernan [Proc. Am. Math. Soc. 22, No. 3, 603–606 (1969; Zbl 0182.11101)].

MSC:
51M99 Real and complex geometry
14N05 Projective techniques in algebraic geometry
32Q45 Hyperbolic and Kobayashi hyperbolic manifolds
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