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

2021/02/04 by Cao, Junyan, Henri Guenancia, Guenancia, Henri +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2102.02744

openalex publication_date 2021/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we obtain various formulas for the curvature of the L² 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 L² metric.

Related

• Positivity of twisted relative pluricanonical bundles and their direct images
• Curvature of higher direct images of sheaves of twisted holomorphic forms
• Positivity of direct images with a Poincaré type twist
• Curvature of higher direct images
• On the boundary behavior of the curvature of L2-metrics