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Hyperbolicity and integral points off divisors in subgeneral position in projective algebraic varieties

Volume 170 / 2015

Do Duc Thai, Nguyen Huu Kien 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 $V\subset \mathbb {P}^{m}_{\mathbb C}.$

Authors

  • Do Duc ThaiDepartment of Mathematics
    Hanoi National University of Education
    136 Xuan Thuy St., Cau Giay, Hanoi, Vietnam
    e-mail
  • Nguyen Huu KienDepartment of Mathematics
    Hanoi National University of Education
    136 XuanThuy St., Cau Giay, Hanoi, Vietnam
    e-mail

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