$L^2$ extension of adjoint line bundle sections

[Extension $L^2$ des sections du fibré en droite ajdoint]

Kim, Dano

Annales de l'Institut Fourier, Tome 60 (2010), p. 1435-1477 / Harvested from Numdam

Résumé

Nous prouvons un théorème d’extension de type Ohsawa-Takegoshi pour les sections du fibré en droite de codimension générale dans une variété projective normale. Notre méthode donne des conditions qui doivent être satisfaites par de telles extensions dans un cadre général, alors qu’elles sont satisfaites quand la sous-variété est donnée par un faisceau d’idéaux multiplicateur approprié.

Abstract

We prove an extension theorem of Ohsawa-Takegoshi type for line bundle sections on a subvariety of general codimension in a normal projective variety. Our method of proof gives conditions to be satisfied for such extension in a general setting, while such conditions are satisfied when the subvariety is given by an appropriate multiplier ideal sheaf.

Détail

Publié le : 2010-01-01

MR 2722247 | Zbl 1207.32011

DOI : https://doi.org/10.5802/aif.2560
Classification:  32J25,  14E30
Mots clés: Extension $L^2$, faisceau d’idéaux multiplicateur, fibré en droite pluricanonique

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