On the number of points of bounded height?on arithmetic projective spaces

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• 作者：Carlo Gasbarri
• 关键词：Mathematics Subject Classification (1991) ; 14G40 ; 14G05 ; 11G35
• 刊名：manuscripta mathematica
• 出版年：1999
• 出版时间：April 1999
• 年：1999
• 卷：98
• 期：4
• 页码：453-475
• 全文大小：155 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Algebraic Geometry
  Topological Groups and Lie Groups
  Geometry
  Number Theory
  Calculus of Variations and Optimal Control
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-1785

文摘

Let K be a number field and its ring of integers. Let be a Hermitian vector bundle over . In the first part of this paper we estimate the number of points of bounded height in (generalizing a result by Schanuel). We give then some applications: we estimate the number of hyperplanes and hypersurfaces of degree d>1 in of bounded height and containing a fixed linear subvariety and we estimate the number of points of height, with respect to the anticanonical line bundle, less then T (when T goes to infinity) of ? N _K blown up at a linear subspace of codimension two.