Distribution of logarithmic spectra of the equilibrium energy

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• 作者：Huayi Chen ; Catriona Maclean
• 关键词：14G40 ; 53C55 ; 32P05
• 刊名：manuscripta mathematica
• 出版年：2015
• 出版时间：March 2015
• 年：2015
• 卷：146
• 期：3-4
• 页码：365-394
• 全文大小：344 KB
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• 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 L be a big invertible sheaf on a projective variety defined on a complete valued field (such as the field \({\mathbb{C}}\) of complex numbers or a complete non-archimedean field), equipped with two continuous metrics. By using the ideas in Arakelov geometry, we prove that the distribution of the eigenvalues of the transition matrix between the L 2 norms on H 0(X,nL) with respect to the two metriques converges (in law) as n goes to infinity to a Borel probability measure on \({\mathbb{R}}\) . This result can be thought of as a generalization of the existence of the energy at the equilibrium as a limit, or an extension of Berndtsson’s results to the more general context of graded linear series and a more general class of line bundles.