Some examples of hyperbolic hypersurfacesin the complex projective space

Abstract

In the previous paper [6], the author constructed hyperbolic hypersurfaces of degree $2^n$ in the $n$-dimensional complex projective space for every $n \geq 3$. The purpose of this paper is to give some improvement of this result and to show some general methods of constructions of hyperbolic hypersurfaces of higher degree, which enable us to construct hyperbolic hypersurfaces of degree $d$ in the $n$-dimensional complex projective space for every $d \geq 2 \times 6^n$.