2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64890In 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.Differential GeometryAlgebraic Geometry53C25; 32Q20text