Dans cette note, nous obtenons diverses formules pour la courbure de la métriques sur l’image directe du fibré canonique relatif tordu par un fibré en droites holomorphe muni d’une métrique à courbure positive avec singularités analytiques, généralisant certains des résultats fondateurs de Berndtsson dans le cas lisse. Quand le fibré par lequel on tord est gros, nous pouvons de plus donner une borne inférieure explicite de la courbure de la métrique .
In this note, we obtain various formulas for the curvature of the metric on the direct image of the relative canonical bundle twisted by a holomorphic line bundle endowed with a positively curved metric with analytic singularities, generalizing some of Berndtsson’s seminal results in the smooth case. When the twist is assumed to be relatively big, we further provide a very explicit lower bound for the curvature of the metric.
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@article{AFST_2022_6_31_3_861_0,
author = {Junyan Cao and Henri Guenancia and Mihai P\u{a}un},
title = {Curvature formula for direct images of twisted relative canonical bundles endowed with a singular metric},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {861--905},
publisher = {Universit\'e Paul Sabatier, Toulouse},
volume = {Ser. 6, 31},
number = {3},
year = {2022},
doi = {10.5802/afst.1707},
language = {en},
url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1707/}
}
TY - JOUR AU - Junyan Cao AU - Henri Guenancia AU - Mihai Păun TI - Curvature formula for direct images of twisted relative canonical bundles endowed with a singular metric JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2022 SP - 861 EP - 905 VL - 31 IS - 3 PB - Université Paul Sabatier, Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1707/ DO - 10.5802/afst.1707 LA - en ID - AFST_2022_6_31_3_861_0 ER -
%0 Journal Article %A Junyan Cao %A Henri Guenancia %A Mihai Păun %T Curvature formula for direct images of twisted relative canonical bundles endowed with a singular metric %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2022 %P 861-905 %V 31 %N 3 %I Université Paul Sabatier, Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1707/ %R 10.5802/afst.1707 %G en %F AFST_2022_6_31_3_861_0
Junyan Cao; Henri Guenancia; Mihai Păun. Curvature formula for direct images of twisted relative canonical bundles endowed with a singular metric. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 31 (2022) no. 3, pp. 861-905. doi : 10.5802/afst.1707. https://afst.centre-mersenne.org/articles/10.5802/afst.1707/
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