Let be a complex manifold and be a holomorphic line bundle on . Assume that is semi-positive, namely admits a smooth Hermitian metric with semi-positive Chern curvature. Let be a compact Kähler submanifold of such that the restriction of to is topologically trivial. We investigate the obstruction for to be unitary flat on a neighborhood of in . As an application, for example, we show the existence of nef, big, and non semi-positive line bundle on a non-singular projective surface.
Soit une variété complexe et un fibré en droites holomorphe sur . Supposons que est semi-positive, à savoir admet une métrique hermitienne lisse avec une courbure de Chern semi-positif. Soit une sous-variété kählérienne compacte de telle que la restriction de à est topologiquement triviale. Nous examinons l’obstruction pour que soit plat unitaire sur un voisinage de . Comme application, par exemple, nous prouvons l’existence d’un fibré en droites nef, grand et non semi-positif sur une surface projective non singulière.
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Keywords: Hermitian metrics, neighborhoods of subvarieties, Ueda theory
Mot clés : métrique hermitienne, voisinage de sous-variété, théorie d’Ueda
Koike, Takayuki 1
@article{AIF_2021__71_5_2237_0, author = {Koike, Takayuki}, title = {Linearization of transition functions of a semi-positive line bundle along a certain submanifold}, journal = {Annales de l'Institut Fourier}, pages = {2237--2271}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {71}, number = {5}, year = {2021}, doi = {10.5802/aif.3439}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3439/} }
TY - JOUR AU - Koike, Takayuki TI - Linearization of transition functions of a semi-positive line bundle along a certain submanifold JO - Annales de l'Institut Fourier PY - 2021 SP - 2237 EP - 2271 VL - 71 IS - 5 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3439/ DO - 10.5802/aif.3439 LA - en ID - AIF_2021__71_5_2237_0 ER -
%0 Journal Article %A Koike, Takayuki %T Linearization of transition functions of a semi-positive line bundle along a certain submanifold %J Annales de l'Institut Fourier %D 2021 %P 2237-2271 %V 71 %N 5 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3439/ %R 10.5802/aif.3439 %G en %F AIF_2021__71_5_2237_0
Koike, Takayuki. Linearization of transition functions of a semi-positive line bundle along a certain submanifold. Annales de l'Institut Fourier, Volume 71 (2021) no. 5, pp. 2237-2271. doi : 10.5802/aif.3439. https://aif.centre-mersenne.org/articles/10.5802/aif.3439/
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