For and , let be an -dimensional irreducible Hermitian symmetric space of compact type and let be the ample generator of . Let be a smooth complete intersection of dimension , where with . We prove a vanishing theorem for twisted holomorphic forms on . As an application, we show that the tangent bundle of is stable. Moreover, if is a smooth hypersurface of degree in such that the restriction is surjective, we establish some effective results for to guarantee the stability of the restriction . In particular, if is a general hypersurface in and is a general smooth divisor in , we show that is stable except for some well-known examples. We also address the cases where the Picard group increases by restriction.
Soient un espace hermitien symétrique irréductible de type compact et de dimension avec et , le générateur ample de . Soit une intersection complète lisse de dimension où avec . Nous montrons un théorème d’annulation pour le faisceau tordu des germes de -formes holomorphes . Comme application, nous montrons que le fibré tangent de est stable. De plus, si est une hypersurface lisse de degré dans telle que la restriction soit surjective, nous obtenons des estimations effectives liées à la stabilité de la restriction . En particulier, si est une hypersurface générale dans et est un diviseur général, nous montrons que est stable sauf certains exemples bien connus. Nous considérons aussi le cas où le nombre de Picard augmente par restriction.
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Keywords: stability, tangent bundle, Lefschetz property, complete intersection, Hermitian symmetric space
Mot clés : stabilité, fibré tangent, propriété de Lefschetz, intersection complète, espace hermitien symétrique
@article{AIF_2021__71_4_1601_0, author = {Liu, Jie}, title = {Stability of the tangent bundles of complete intersections and effective restriction}, journal = {Annales de l'Institut Fourier}, pages = {1601--1634}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {71}, number = {4}, year = {2021}, doi = {10.5802/aif.3435}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.3435/} }
TY - JOUR AU - Liu, Jie TI - Stability of the tangent bundles of complete intersections and effective restriction JO - Annales de l'Institut Fourier PY - 2021 SP - 1601 EP - 1634 VL - 71 IS - 4 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.3435/ DO - 10.5802/aif.3435 LA - en ID - AIF_2021__71_4_1601_0 ER -
%0 Journal Article %A Liu, Jie %T Stability of the tangent bundles of complete intersections and effective restriction %J Annales de l'Institut Fourier %D 2021 %P 1601-1634 %V 71 %N 4 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.3435/ %R 10.5802/aif.3435 %G en %F AIF_2021__71_4_1601_0
Liu, Jie. Stability of the tangent bundles of complete intersections and effective restriction. Annales de l'Institut Fourier, Volume 71 (2021) no. 4, pp. 1601-1634. doi : 10.5802/aif.3435. http://www.numdam.org/articles/10.5802/aif.3435/
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