Calabi Energies of Extremal Toric Surfaces
arXiv:1110.0682
Abstract
We derive a formula for the L^2 norm of the scalar curvature of any extremal Kaehler metric on a compact toric manifold, stated purely in terms of the geometry of the corresponding moment polytope. The main interest of this formula pertains to the case of complex dimension 2, where it plays a key role in construction of Bach-flat metrics on appropriate 4-manifolds.
28 pages. Published version. Added section on Abreu formalism generalizes main result to higher dimensions