Convergence de la mêtrique de Fubini-Study d'un fibré linéaire positif. (Convergence of the Fubini-Study metric of a positive line bundle.)
type: Item
instance of: scholarly article
title: Convergence de la mêtrique de Fubini-Study d'un fibré linéaire positif. (Convergence of the Fubini-Study metric of a positive line bundle.)
zbMATH Open document ID: 0685.32015
author: Thierry Bouche
publication date: 1990-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/74866
review text: Let E be a positive line bundle over a compact complex manifold. We show that the distortion function defined by the quotient of the initial metric by the Fubini-Study metric of \(E^{\otimes k}\) admits an equivalent when k tends to infinity. This improves the previous inequalities given by Kempf and Ji over Abelian varieties, and extends them to any projective manifold. The proof rests upon the computation of an equivalent for the heat kernel, with control of the convergence with respect to the time parameter.
Mathematics Subject Classification ID: 32L10
Mathematics Subject Classification ID: 35P10
zbMATH DE Number: 4122325
zbMATH Keywords: positive holomorphic line bundle
zbMATH Keywords: Fubini-Study metric
zbMATH Keywords: kernel
MaRDI profile type: Publication
OpenAlex ID: W2002327995
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DOI: 10.5802/AIF.1206
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 4122325