Journal of Symplectic Geometry

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

Rosa Sena-Dias

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Abstract

We 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.

Article information

Source
J. Symplectic Geom., Volume 8, Number 2 (2010), 119-142.

Dates
First available in Project Euclid: 15 July 2010

Permanent link to this document
https://projecteuclid.org/euclid.jsg/1279199212

Mathematical Reviews number (MathSciNet)
MR2670162

Zentralblatt MATH identifier
1194.14074

Citation

Sena-Dias, Rosa. Spectral measures on toric varieties and the asymptotic expansion of Tian-Yau-Zelditch. J. Symplectic Geom. 8 (2010), no. 2, 119--142. https://projecteuclid.org/euclid.jsg/1279199212


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