Linearization of transition functions of a semi-positive line bundle along a certain submanifold
[Linéarisation des fonctions de transition d’un fibré en droites semi-positif le long d’une certaine sous-variété]
Annales de l'Institut Fourier, Online first, 35 p.

Soit X une variété complexe et L un fibré en droites holomorphe sur X. Supposons que L est semi-positive, à savoir L admet une métrique hermitienne lisse avec une courbure de Chern semi-positif. Soit Y une sous-variété kählérienne compacte de X telle que la restriction de L à Y est topologiquement triviale. Nous examinons l’obstruction pour que L soit plat unitaire sur un voisinage de Y. 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.

Let X be a complex manifold and L be a holomorphic line bundle on X. Assume that L is semi-positive, namely L admits a smooth Hermitian metric with semi-positive Chern curvature. Let Y be a compact Kähler submanifold of X such that the restriction of L to Y is topologically trivial. We investigate the obstruction for L to be unitary flat on a neighborhood of Y in X. As an application, for example, we show the existence of nef, big, and non semi-positive line bundle on a non-singular projective surface.

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DOI : https://doi.org/10.5802/aif.3439
Classification : 32J25,  14C20
Mots clés : métrique hermitienne, voisinage de sous-variété, théorie d’Ueda
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Koike, Takayuki. Linearization of transition functions of a semi-positive line bundle along a certain submanifold. Annales de l'Institut Fourier, Online first, 35 p.

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