Hyperbolic surfaces in ${\mathbb P}^3(\mathbb C)$

Abstract:

We show a class of perturbations $X$ of the Fermat hypersurface such that any holomorphic curve from $\mathbb C$ into $X$ is degenerate. Applying this result, we give explicit examples of hyperbolic surfaces in $\mathbb P^3(\mathbb C)$ of arbitrary degree $d\ge 22$, and of curves of arbitrary degree $d\ge 19$ in $\mathbb P^2(\mathbb C)$ with hyperbolic complements.