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Article Dans Une Revue Manuscripta mathematica Année : 2015

Distribution of logarithmic spectra of the equilibrium energy

Huayi Chen
Catriona Maclean

Résumé

Let $L$ be a big invertible sheaf on a complex projective variety, equipped with two continuous metrics. 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. Our approach also enables us to obtain a $p$-adic analogue of our main result.
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Dates et versions

hal-00816341 , version 1 (21-04-2013)
hal-00816341 , version 2 (21-09-2013)
hal-00816341 , version 3 (14-10-2013)

Identifiants

Citer

Huayi Chen, Catriona Maclean. Distribution of logarithmic spectra of the equilibrium energy. Manuscripta mathematica, 2015, 146 (3-4), pp.365-394. ⟨10.1007/s00229-014-0712-8⟩. ⟨hal-00816341v3⟩

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