Scalar curvature, moment maps and the Deligne Pairing

2002/09/09 by D. H. Phong, Phong, D. H., Jacob Sturm +1
Mathematics · Physics and Astronomy · #32Q20 #53C25 #Advanced Differential Geometry Research #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.AG #math.DG #msc:32Q20 #msc:53C25

paper · pdf · doi:10.48550/arxiv.math/0209098

openalex publication_date 2002/09/09 · arxiv created 2003/12/31 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we the improve the bound for the moment map derivative proved by Donaldson in his recent proof of the Hilbert-Mumford stability of complex manifolds with constant scalar curvature. The proof depends on the identification of Donaldson's symplectic form with the curvature of a certain Deligne pairing.

Citations

• Stability, energy functionals, and Kähler-Einstein metrics

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