Spectral measures on toric varieties and the asymptotic expansion of Tian-Yau-Zelditch

摘要

We extend a recent result of Burns, Guillemin and Uribe on the asymptotics ofthe spectral measure for the reduction metric on a toric variety to any toricmetric on a toric variety. We show how this extended result together with theTian-Yau-Zelditch asymptotic expansion can be used to deduce Abreu's formulafor the scalar curvature of a toric metric on a toric variety in terms ofpolytope data.