# Quelques applications des méthodes effectives en géométrie analytique

Abstract : We generalize first the Ohsawa-Takegoshi-Manivel $L^2$ extension theorem to the case of jets of sections of Hermitian holomorphic line bundles on weakly pseudoconvex Kähler manifolds. Then we give a new simple proof of a theorem of Uhlenbeck and Yau that was the main technical difficulty in their proof of the Kobayashi-Hitchin correspondence on compact Kähler manifolds. This is done via a $(1,1)$-current interpreted a posteriori as the curvature current of some quotient bundle. Thirdly, we investigate a conjecture on the existence of regularizations of closed almost positive currents whose Monge-Ampère masses are under control on a compact not necessarily Kähler manifold. This would yield a new characterization of Moishezon manifolds generalizing those of Siu and Demailly given in response to the Grauert-Riemenschneider conjecture. We give a uniform estimate of the loss of positivity in Demailly's regularization-of-currents theorem and an effective version of the global generation property of multiplier ideal sheaves on pseudoconvex open sets of $(\bf C)^n.$
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Document type :
Theses
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https://tel.archives-ouvertes.fr/tel-00004007
Contributor : Arlette Guttin-Lombard <>
Submitted on : Wednesday, December 17, 2003 - 3:24:58 PM
Last modification on : Wednesday, November 4, 2020 - 1:59:43 PM
Long-term archiving on: : Wednesday, September 12, 2012 - 12:05:31 PM

### Identifiers

• HAL Id : tel-00004007, version 1

### Citation

Dan Popovici. Quelques applications des méthodes effectives en géométrie analytique. Mathématiques [math]. Université Joseph-Fourier - Grenoble I, 2003. Français. ⟨tel-00004007⟩

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