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Pré-Publication, Document De Travail Année : 2021

Curvature formula for direct images of twisted relative canonical bundles endowed with a singular metric

Résumé

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.
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Dates et versions

hal-03132109 , version 1 (04-02-2021)
hal-03132109 , version 2 (14-03-2023)

Identifiants

  • HAL Id : hal-03132109 , version 1

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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. 2021. ⟨hal-03132109v1⟩
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