Kobayashi hyperbolic imbeddings into toric varieties

Abstract

Our main goal of this article is to give a characterization of an algebraic divisor on an algebraic torus whose complement is Kobayashi hyperbolically imbedded into a toric projective variety. As an application of our main theorem, we prove the following: the complement of the union of n + 1 hyperplanes in the n-dimensional projective space \({\mathbb{P}^{n}(\mathbb{C})}\) in general position and a general hypersurface of degree n in \({\mathbb{P}^n(\mathbb{C})}\) is Kobayashi hyperbolically imbedded into \({\mathbb{P}^n(\mathbb{C})}\).