2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/156078We extend a recent result of Burns, Guillemin and Uribe on the asymptotics of the spectral measure for the reduction metric on a toric variety to any toric metric on a toric variety. We show how this extended result together with the Tian-Yau-Zelditch asymptotic expansion can be used to deduce Abreu's formula for the scalar curvature of a toric metric on a toric variety in terms of polytope data.21 pagesDifferential GeometrySymplectic Geometrytext