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

Abstract : 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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https://hal.archives-ouvertes.fr/hal-03132109
Contributor : Henri Guenancia <>
Submitted on : Thursday, February 4, 2021 - 6:16:48 PM
Last modification on : Tuesday, February 9, 2021 - 3:29:09 AM

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  • 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-03132109⟩

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