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.
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.
Keywords: $L^2$ extension, multiplier ideal sheaf, pluricanonical line bundle
Mot clés : Extension $L^2$, faisceau d’idéaux multiplicateur, fibré en droite pluricanonique
Kim, Dano 1
@article{AIF_2010__60_4_1435_0, author = {Kim, Dano}, title = {$L^2$ extension of adjoint line bundle sections}, journal = {Annales de l'Institut Fourier}, pages = {1435--1477}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {60}, number = {4}, year = {2010}, doi = {10.5802/aif.2560}, mrnumber = {2722247}, zbl = {1207.32011}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2560/} }
TY - JOUR AU - Kim, Dano TI - $L^2$ extension of adjoint line bundle sections JO - Annales de l'Institut Fourier PY - 2010 SP - 1435 EP - 1477 VL - 60 IS - 4 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2560/ DO - 10.5802/aif.2560 LA - en ID - AIF_2010__60_4_1435_0 ER -
%0 Journal Article %A Kim, Dano %T $L^2$ extension of adjoint line bundle sections %J Annales de l'Institut Fourier %D 2010 %P 1435-1477 %V 60 %N 4 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2560/ %R 10.5802/aif.2560 %G en %F AIF_2010__60_4_1435_0
Kim, Dano. $L^2$ extension of adjoint line bundle sections. Annales de l'Institut Fourier, Volume 60 (2010) no. 4, pp. 1435-1477. doi : 10.5802/aif.2560. https://aif.centre-mersenne.org/articles/10.5802/aif.2560/
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