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Curvature formula for direct images of twisted relative canonical bundles endowed with a singular metric
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 31 (2022) no. 3, pp. 861-905.

In this note, we obtain various formulas for the curvature of the L 2 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 L 2 metric.

Dans cette note, nous obtenons diverses formules pour la courbure de la métriques L 2 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 L 2 .

Published online:
DOI: 10.5802/afst.1707
Junyan Cao 1; Henri Guenancia 2; Mihai Păun 3

1 Laboratoire de Mathématiques J.A. Dieudonné, UMR 7351 CNRS, Université Côte d’Azur, Parc Valrose, 06108 Nice Cedex 02, France
2 Institut de Mathématiques de Toulouse; UMR 5219, Université de Toulouse; CNRS, UPS, 118 route de Narbonne, F-31062 Toulouse Cedex 9, France
3 Institut für Mathematik, Universität Bayreuth, 95440 Bayreuth, Germany
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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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, Serie 6, Volume 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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