Distribution of logarithmic spectra of the equilibrium energy
type: Item
instance of: scholarly article
title: Distribution of logarithmic spectra of the equilibrium energy
zbMATH Open document ID: 1400.14071
author: Catriona Maclean
author: Huayi Chen
published in: Manuscripta Mathematica
publication date: 2015-03-23T00:00:00Z
full work available at URL: https://arxiv.org/abs/1304.5842
review text: Let \(X\) be a projective variety defined on a complete valued field, and let \(L\) be a big line bundle on \(X\). Suppose that this line bundle \(L\) is equipped with two continuous metrics. In the paper under review, the authors show that the distribution of the eigenvalues of the transition matrix between the \(L^2\)-norms on \(H^0(X,nL)\) with respect to these two metrics converges (in law) as \(n\to \infty\) to a Borel probability measure on \(\mathbb{R}\). This result is proved using the ideas from Arakelov geometry, and it can be viewed 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.
reviewed by: Shun Tang
Mathematics Subject Classification ID: 14G40
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 32P05
zbMATH DE Number: 6418372
zbMATH Keywords: distribution
zbMATH Keywords: logarithmic spectra
zbMATH Keywords: equilibrium energy
zbMATH Keywords: probability measure
MaRDI profile type: Publication
OpenAlex ID: W2035114410
arXiv ID: 1304.5842
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DOI: 10.1007/S00229-014-0712-8
description: scientific article