The hyperbolicity of the complement of $2n+1$ hyperplanes in general position in $P_{n}$ and related results

Abstract:

Using a modified version of a technique of R. Brody, a simple proof is found that the complement of 2n + 1 hyperplanes in general position in ${{\mathbf {P}}_n}$ is complete hyperbolic and hyperbolically embedded in ${{\mathbf {P}}_n}$. In fact, a more general result is obtained showing that a suitable Picard theorem is sufficient to imply hyperbolicity in a large class of algebro-geometric situations.