Hyperbolicity and integral points off divisors in subgeneral position in projective algebraic varieties
Volume 170 / 2015
Acta Arithmetica 170 (2015), 231-242
MSC: Primary 11J97; Secondary 32H30, 11D57.
DOI: 10.4064/aa170-3-2
Abstract
The purpose of this article is twofold. The first is to find the dimension of the set of integral points off divisors in subgeneral position in a projective algebraic variety $V\subset \mathbb {P}^{m}_{\overline {k}},$ where $k$ is a number field. As consequences, the results of Ru–Wong (1991), Ru (1993), Noguchi–Winkelmann (2003) and Levin (2008) are recovered. The second is to show the complete hyperbolicity of the complement of divisors in subgeneral position in a projective algebraic variety $V\subset \mathbb {P}^{m}_{\mathbb C}.$
