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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