Seshadri constants, diophantine approximation, and Roth's theorem for arbitrary varieties

• 成果类型: Article
• 署名作者: McKinnon, David; Roth, Mike
• 署名单位: University of Waterloo; Queens University - Canada
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-014-0540-1
• 发表日期: 2015
• 页码: 513-583
• 关键词: divisors

摘要

In this paper, we associate an invariant to an algebraic point on an algebraic variety with an ample line bundle . The invariant measures how well can be approximated by rational points on , with respect to the height function associated to . We show that this invariant is closely related to the Seshadri constant measuring local positivity of at , and in particular that Roth's theorem on generalizes as an inequality between these two invariants valid for arbitrary projective varieties.