$L^2$ extension of adjoint line bundle sections

Kim, Dano

Annales de l'Institut Fourier, Tome 60 (2010) no. 4, pp. 1435-1477.

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.

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.

Classification : 32J25, 14E30
Keywords: $L^2$ extension, multiplier ideal sheaf, pluricanonical line bundle
Mot clés : Extension $L^2$, faisceau d’idéaux multiplicateur, fibré en droite pluricanonique

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